J.  Henry  Senger 


SOLUTIONS  OF  PROBLEMS 


GE'S  ELEMENTS  OF  PHYSICS. 


\  GENERAL  REVIEW,  TEST  QUESTIONS,  AND 
HINTS  TO  TEACH EKS. 


!.,  IV.,  A>T)'V.  OF  ins  "PHYSICAL  Tr,<:uxr< 

,  >K) . 


BOSTON: 

PUBLISHED   BY   GIXN,    HEATH,    &   Co. 

188$. 


CHEMISTRY, 

An  Introduction  to  the  Study  of  the  Com- 

pounds  of  Carbon,  or  Organic  Chemistry. 

By  "Prof.  IRA  REMSEN,  Johns  Hopkins  University,  Baltimore. 

The  book,  which  is  strictly  an  introduction  to  the  study  of 
the  Compounds  of  Carbon,  or  Organic  Chemistry,  is  intended  to 
meet  the  \vants  of  the  students  in  our  scientific  schools,  school.; 
of  technology  and  colleges,  and  of  medical  students.  It  is  per- 
haps'rather  more  elementary  than  most  of  the  existing  small 
books  on  the  subject,  and  is  hence,  it  is  believed,  better  adapted 
to  the  classes  of  students  mentioned.  It  takes  nothing  for 
grfented  except  an  elementary  knowledge  of  General  Chemistry, 
and  explains  pretty  fully  the  methods  of  thought  used  in  dealing 
with  the  subject,- and  the  connection  between  the  facts  and  the 
prevailing  hypotheses.  The  attempt  has  not  been  made  to 
describe  or  even  mention  most  of  the  compounds  of  carbon, 
but  all  which  are  of  real  importance  to  the  beginner  are  treated 
of  with  some  degree  of  fulness.  Thus  there  is  less  danger  of 
confusion  than  when  a  larger  number  is  brought  to  the  attention 
of  the  student.  Full  directions  are  given  for  making  a  number 
of  typical  compounds,  by  methods  quite  within  the  reach  of 
every  chemical  laboratory,  so  that  with  the  aid  of  the  book  a 
systematic  course  of  laboratory  work  on  carbon  compound3  may 
be  carrild  on.  \Rcady  March  i. 

Elements  of  Descriptive  and  Qualitative 

Inorganic  Chemistry. 

Adapted  to  the  use  of  High  Schools  and  Academies.     By  JAMES  IT. 

SHEPARD,  Instructor  in  Chemistry,  Ypsilanti  High  School. 

The  tendency  toward  practical  work  in  place  of  mere  book- 
teaching  is  everywhere  evinced  by  the  establishing  of  Laboratories 
both  Physical  and  Chemical,  not  only  in  our  higher  institutions 
of  learning,  but  also  in  our  progressive  preparatory  schools. 

Chemistry  is  one.  of  the  most  practical  studies,  and  is  espe- 
cially fortunate  in  the  richness  of  the  material  from  which  to 
draw. 

The  author  "has  devoted  himself  entirely  to  the  work  and 
heeds  of  the  class  of  schools  for  which  this  treatise  has  been 
prepared.  He  has  deviated  from  the  ordinary  course  hitherto 
pursued,  by  treating  conjointly  General  Descriptive  and  Quali- 
tative work  in  one  volume,  thus  allowing  these  kindred  branches 


SOLUTIONS  OF  PEOBLEMS 


GAGE'S  ELEMENTS  OF  PHYSIOS. 


A  GENERAL  REVIEW,  TEST  QUESTIONS,  AND 
HINTS  TO  TEACHERS. 


PARTS  III.,  IV.,  AND  V.  OF  HIS  "  PHYSICAL  TECHNICS," 
(PUBLISHED  BY  THE  AUTHOR). 


BOSTON: 

PUBLISHED   BY   GINN,   HEATH,   &   CO. 

1885. 


'• '          •   *»EnCe&dSicWding  to  Act  of  Congress,  In  the  year  1884,  by 

•I :' I  -*•**!•     I  .*.  *" 'ALFRED  p.  GAGE, 

"  •*  *  r '"    id  the  Office  of  tne  Librarian  of  Congress,  at  Washington. 


J.  S.  CUSHING  &s  Co.,  PRINTEBS,  115  HIGH  STREET,  BOSTON. 


PAET  III. 

GENERAL   REVIEW   OF  PHYSICS,  WITH 
HINTS  TO   TEACHERS. 


CHAPTER  I. 

PROPERTIES   OP   MATTER. 

§  1,  p.  1.  The  pupil  maybe  informed  that,  though  the  defini- 
tion here  given  of  an  experiment  harmonizes  with  its  etymolo- 
gical signification  and  with  the  general  spirit  of  this  book,  yet 
it  is  frequently  used  as  a  synonym  for  illustration  or  proof. 

P.  3,  Exp.  5.  The  apparatus  furnished  for  this  experiment  is 
so  sensitive  that  sufficient  air  can  be  drawn  from  the  globe  by 
suction  with  the  mouth  to  cause  the  beam  to  tip  perceptibly. 
A  change  in  weight  will  be  still  more  perceptible  if,  after  ex- 
hausting the  air  by  suction,  a  person  were  to  condense  air  in 
the  globe  by  blowing  into  it,  and  then  closing  the  stop-cock. 

§  4,  p.  4.  "The  molecules  of  the  same  substance  are  all 
exactly  alike,  but  different  from  those  of  other  substances. 
Molecules  are  unalterable  by  any  of  the  processes  which  go 
on  in  the  present  state  of  things,  and  every  individual  of  each 
species  is  of  exactly  the  same  magnitude  as  though  they  had 
all  been  cast  in  the  same  mould,  like  bullets,  and  not  merely 
selected  and  grouped  according  to  their  size,  like  small  shot. 

They  are,  as  we  believe,  the  only  material  things  which  still 
remain  in  the  precise  condition  in  which  they  first  began  to 
exist."  —  MAXWELL. 

§  5,  p.  G.  The  pupil  may  be  aided  in  applying  this  theory  to 
the  condition  of  things  supposed  to  exist,  for  instance,  in  the 


182  GENERAL   REVIEW   OF   PHYSICS. 

test-tube  of  §  4  filled  with  water,  by  imagining  that  he  is  look- 
ing at  a  dense  flock  of  birds  in  the  air.  The  flock  remains  at 
rest,  but  the  individuals  which  compose  the  flock  are  in  rapid 
motion,  frequently  hitting  and  bounding  away  from  one  another. 
At  the  same  time  he  sees  the  whole  atmosphere  filled  with  birds 
of  a  different  hue.  These  birds,  like  the  former,  are  in  constant 
motion.  Some  are  constantly  entering  the  space  occupied  by 
tii(*  floclt,  Arid:  spine:  are  leaving  it,  while  all  are  jostling  against 
one  ariotiierv'  "tfre  Blatter  birds  are  nowhere  nearly  so  thick 
,  £&£»{  Ah'ere  ftre'no-t  so';inany  in  a  given  unit  of  space)  as  those 
which  compose 't'he' flock,  but  they  are  thicker  in  the  space  oc- 
cupied by  the  flock  than  in  the  space  outside  the  flock,  partly 
because  their  escape  from  this  space  is  impeded  by  the  presence 
of  the  birds  of  the  flock,  and  partly  because  of  some  mutual 
attraction  or  affiliation. 

The  birds  constituting  the  flock  may  represent  the  molecules 
composing  the  body  of  water  in  the  test-tube ;  while  the  birds 
of  different  hue  ma}'  represent  the  air  molecules.  Beware  of 
the  common  error  of  supposing  that  the  latter  are  smaller  than 
the  former,  as  in  the  oft-given  but  fallacious  illustration  of 
"  apples,  marbles,  and  bird-shot."  Apprise  the  pupil  of  the 
fact  that  air  in  water  is  in  a  comparatively  condensed  state  ;  in 
other  words,  that  a  tumbler  filled  with  water  contains  more  air 
than  it  would  contain  if  no  water  were  in  the  tumbler. 

§  7,  p.  7.  LAW  OF  AWOGADRO.  — All  gases  (at  the  same  tem- 
perature and  pressure)  consist,  within  equal  volumes,  of  equal 
numbers  of  molecules. 

Exp.  2,  p.  10.  This  may  well  be  made  a  home-experiment, 
and  performed  as  follows :  On  two  piles  of  books  about  lO0"1 
apart  support  a  tin  basin  containing  about  a  liter  of  ice-water 
and  a  few  lumps  of  ice.  Between  the  piles  and  under  the  basin 
place  a  lighted  candle,  so  that  the  tip  of  the  flame  will  just 
touch  the  basin.  The  books,  besides  serving  as  a  support,  will 
protect  the  flame  from  currents  of  air.  In  10  or  15  minutes  the 
bottom  of  the  basin,  except  a  small  area  immediately  over  the 


CHAPTER   I.  —  PROPERTIES    OF   MATTER.  133 

flame,  will  be  covered  with  large  drops  of  water,  and  a  stalac- 
tite of  carbon  will  depend  from  the  basin  immediately  above 
the  flame.  After  the  pupil  has  performed  this  experiment  he 
should  be  plied  with  such  questions  an  follows  :  — 

Whence  came  the  water  and  the  carbon  ?  What  purpose  does 
the  ice-water  serve  ?  Whence  comes  the  water  frequently  found 
on  sweating  ice-pitchers  ?  How  do  you  know  that  the  water 
found  on  the  bottom  of  the  basin  did  not  come  from  the  same 
source  ?  Would  the  heat  of  the  flame  tend  to  increase  or  retard 
this  condensation?  Does  carbon  always  rise  from  a  burning 
candle  flame  ?  Why  does  it  collect  in  such  abundance  in  this 
case  ?  What  are  the  ashes  of  the  candle  ? 

§  11,  p.  12,  Exp.  1.  Inasmuch  as  the  success  of  this  ex- 
periment depends  frequently  upon  the  condition  of  the  apparatus 
and  the  state  of  the  weather,  the  following  substitute  will  be 
found  very  convenient :  Take  a  cork  about  lcm  in  diameter, 
and  cut  it  transversely  into  slices  about  lmm  thick.  Then  take 
four  cambric  needles,  break  them  in  the  middle,  rub  each  piece 
two  or  three  times  in  the  same  direction  across  the  same  pole  of 
a  magnet,  and  thrust  each  piece  perpendicularly  through  a  cork 
slice,  leaving  one  extremity  level  with  the  surface  of  the  cork. 
Be  sure  that  the  ends  which  are  inserted  in  the  corks  are  all  the 
same  poles,  i.e.,  all  S.  or  all  N.  poles.  Fill  a  bowl  or  goblet 
with  water  to  the  brim,  and  float  the  slices  on  the  surface  of 
the  water,  with  the  projecting  part  of  the  needle  immersed  in 
the  water.  Holding  a  bar-magnet  vertically,  approach  the 
center  of  the  surface  of  the  water  with  one  of  its  poles,  and 
the  slices  of  cork  will  sail  along  the  surface,  either  collecting 
under  this  pole  of  the  magnet  or  receding  from  it.  Reverse 
the  pole  of  the  magnet,  and  the  phenomenon  will  be  reversed. 

§  17,  p.  18.  The  native  of  Borabora  who  called  hail  "•  white 
stones  "  spoke  the  simple  truth.  Ice  is  stone,  a  mineral,  in 
every  sense  which  these  terms  imply.  In  the  year  1739,  at  the 
wedding  of  Prince  Gallitzin,  the  Russians  built  for  him  a  house 
of  large  blocks  of  stone.  All  the  furniture  of  the  house,  even 


184  GENERAL   REVIEW    OF   PHYSICS. 

to  the  nuptial  bed,  was  made  of  the  same  stone  ;  and  the  cannon 
and  mortars  which  were  fired  in  honor  of  the  day  were  con- 
structed of  the  same.  The  mineralogical  name  of  this  stone  is 
—  ice. 

§  17,  p.  20.  "  According  to  Pictet,  oxygen  is  liquefied  at  320 
atmospheres  pressure  and  —  140°  C.  ;  and  then,  upon  allowing 
a  jet  of  this  liquid  to  escape  into  the  air,  the  escaping  jet  of 
liquid  oxygen  becomes  extremely  cold  and  is  partly  solidified. 
Hydrogen  treated  in  a  similar  manner,  under  a  pressure  of  650 
atmospheres,  appeared  as  a  steel-blue  stream  of  liquid,  the  light 
reflected  from  which,  being  partly  polarized,  revealed  the  pres- 
ence of  solid  particles  in  the  liquid,  while  the  tube  of  exit 
became  blocked  with  solid  hydrogen."  —  DANIELL. 

Full   accounts   of  the   liquefaction  and  solidification  of  the 

u  permanent   gases "    can   be   found   in   the    Popular   Science 

Monthly,  Scientific  American,  and  Nature,  of  the  year  1878. 

§  21,  p.  22.     It  may  be  demonstrated  geometrically  that  a 

particle  placed  anywhere,  as  A,  A',  A",  etc.,  Fig.  18,  within 

a  homogeneous  spherical  shell 
will  be  in  equilibrium.  Conse- 
quently,  if  the  earth  were  such 
a  shell,  a  body  placed  anywhere 
within  it  would  remain  at  rest. 
Fi  is  "*"~=*s=^  Hence,  it  follows  that  if  the 
earth  were  a  homogeneous  solid 
sphere,  the  weight  of  any  body  within  it,  as  J5,  Fig.  18,  would 
vary  as  its  distance  from  the  center  (7,  and  wculd  be  entirely 
independent  of  the  external  shell,  as  ED. 

P.  25.  In  performing  Exp.  1  notice  the  difference  in  the 
crystals  formed  on  the  thread  and  those  formed  on  the  bottom 
of  the  vessel.  The  latter  are  said  to  be  tabulated. 

In  performing  Exp.  2  watch  the  growth  of  the  cr}~stals,  look- 
ing through  a  simple  microscope.  In  their  note-books  pupils 
may  draw  figures  of  the  crystals  formed,  both  of  a  single  crystal, 
and  of  a  group  of  crystals,  selecting  the  most  interesting. 


CHAPTER    I.  —  PROPERTIES    OF   MATTER.  135 

§  25,  p.  2G.  Repeat  the  experiment  with  the  bar-magnet  and 
floats  (p.  133),  and  notice  that  when  the  floats  are  attracted  to 
one  end  of  the  magnet,  through  the  influence  of  their  polarit}*, 
they  arrange  themselves  in  some  regular  geometrical  form,  i.e., 
in  squares,  pentagons,  hexagons,  etc.  This  phenomenon  is  as 
significant  as  it  is  interesting. 

§  28,  p.  31.  Strain.  In  physics  any  alteration  of  size  or 
shape  whatever  is  called  a  strain.  It  includes  all  alterations  in 
volume,  —  as  compression  or  expansion  of  gases,  —  all  twist- 
ings  and  beudings,  and  all  extensions,  as  a  piece  of  stretched 
india-rubber. 

§  30,  p.  31.  Viscosity.  "  If  a  constant  stress  causes  a  strain 
or  displacement  in  the  body,  which  increases  continually  with 
the  time,  the  substance  is  said  to  be  viscous. 

u  When  this  continuous  alteration  of  form  is  only  produced 
by  stresses  exceeding  a  certain  value,  the  substance  is  called  a 
solid,  however  soft  it  may  be.  When  the  very  smallest  stress, 
if  continued  long  enough,  will  cause  a  constantly  increasing 
change  of  form,  the  body  must  be  regarded  as  a  viscous  fluid, 
however  hard  it  may  be. 

"  Thus,  a  tallow  candle  is  much  softer  than  a  stick  of  sealing- 
wax  ;  but  if  the  candle  and  the  stick  of  sealing-wax  are  laid 
horizontally  between  two  supports,  the  sealing-wax  will  in  a  few 
weeks  in  summer  bend  with  its  own  weight,  while  the  candle 
remains  straight.  The  caudle  is  therefore  a  soft  solid,  and  the 
sealing-wax  a  very  viscous  fluid. 

"  What  is  required  to  alter  the  form  of  a  soft  solid  is  a  suf- 
ficient force  ;  and  this,  when  applied,  produces  its  effect  at  once. 
In  the  case  of  a  viscous  fluid,  it  is  time  which  is  required  ;  and,  if 
enough  time  is  given,  the  very  smallest  force  will  produce  a  sen- 
sible effect,  such  as  would  require  a  very  large  force  if  suddenly 
applied."  —  MAXWELL. 

§  33,  p.  33.  Adhesion.  In  both  experiments  with  the  water 
and  the  mercury  it  is  important  that  the  glass  slip  should  be 
quite  clean.  It  is  well,  previous  to  each  experiment,  to  wipe 


136 


GENERAL   REVIEW   OF   PHYSICS. 


the  glass  and  the  surface  of  the  mercury  with  a  dry,  clean  cloth, 
so  as  to  remove  any  oxide  of  mercury  which  may  rest  upon  their 
surfaces. 


CHAPTER     II. 

DYNAMICS. 

P.  47.  If  the  author's  "  Seven-in-one"  apparatus  is  sub- 
stituted for  the  Magdeburg  hemispheres,  no  air-pump  will  be 
needed,  and  no  mystery,  which  its  action  and  the  necessity  for 
removal  of  air  might  cause,  will  be  introduced.  If  the  piston 
of  this  apparatus  is  forced  into  the  end  of  the  cylinder,  and  the 
stop-cock  is  closed  so  as  to  prevent  air  entering  the  apparatus, 
a  weight  of  two  or  three  hundred  pounds  may  be  suspended 
from  the  piston  without  drawing  it  down.  But  if  air  is  admitted, 
by  turning  the  stop-cock  so  as  to  press  on  both  sides  of  the 
piston,  it  will  quickly  descend. 

§  46,  p.  48.  Apparatus  for  exploration  of  pressure  in  the 
interior  of  a  liquid  mass.  A  very  convenient  substitute  for  the 
apparatus  represented  in  Fig.  27  is  a  glass  manom- 
eter tube,  represented  in  Fig.  19.  Mercury  or  some 
lighter  colored  liquid  may  be  used  in  the  tube :  the 
lighter  the  liquid  the  more  sensitive  will  be  the  instru- 
ment. Connecting  a  short  rubber  tube  with  the  ex- 
tremity a  of  the  glass  tube,  and  bending  it  in  different 
directions,  pressure  in  all  directions  and  at  different 
depths  can  be  explored  and  compared. 

§  50,  p.  57.  Mariotte's  Law  Apparatus.  In  the 
preparation  of  this  apparatus  for  use  there  is  usually 
some  difficulty  in  getting  the  surfaces  of  the  mercury 
in  the  two  arms  of  the  tube  on  the  same  level.  This  may  be 
accomplished,  however,  after  a  few  trials,  by  tipping  the  tube, 
and  either  admitting  small  bubbles  of  air  into  the  short  arm,  or 
excluding  it  therefrom,  as  the  case  may  require. 


Fig.  19. 


CHAPTER   II. —  DYNAMICS.  187 

The  base  of  the  tube  (Fig.  38)  is  sufficiently  large  to  receive 
the  tube  (Fig.  39),  hence  it  will  answer  for  the  jar  B  in  Exp.  2. 

§  52,  p.  61.  In  using  the  apparatus  illustrated  in  Fig.  46, 
very  likely  the  stream  issuing  from  the  longest  tube  d  may  not 
quite  reach  the  level  of  the  top  of  the  other  streams.  This  is 
to  be  explained  as  the  result  of  the  friction  against  the  sides  of 
the  longer  tube,  the  friction  increasing  with  the  length  of  the 
tube. 

§  53,  p.  64.  In  using  the  Seven-in-one  apparatus  as  a  hydro- 
static bellows,  the  piston  should  be  forced  into  the  cylinder,  and 
the  space  between  the  piston  and  the  end  of  the  cylinder  should 
be  filled  with  water.  This  may  be  done  by  temporarily  remov- 
ing the  rubber  tube.  If  there  is  any  difficulty  in  removing  the 
air  from  the  tube,  so  as  to  allow  the  water  to  enter  it,  the  tube 
may  be  first  filled  with  water,  and,  while  in  a  nearly  horizontal 
position,  be  connected  with  the  union-screw,  and  afterwards 
raised  to  a  vertical  position. 

§  55,  p.  67.  In  using  the  improved  Pascal's  Vases,  support 
the  base  upon  the  side  of  a  water  pail.  Attach  to  it  first  the 
vase  corresponding  to  C,  Fig.  52.  Suspend  the  disk  d  from 
one  arm  of  the  balance-beam,  and  the  counterpoise  from  one  of 
the  holes  in  the  other  arm.  Pour  water  slowly  into  the  vase, 
allowing  it  to  trickle  down  its  side,  at  the  same  time  elevating 
the  nut  on  the  rod  supporting  the  disk  so  as  to  keep  it  on  a 
level  with  the  surface  of  the  water.  Continue  to  pour  water 
until  it  forces  the  bottom  off.  Then  remove  the  vase  from  the 
base  and  substitute  the  cylinder  A.  Now,  if  water  is  carefully 
poured  into  the  cylinder,  it  will  be  found  that  the  bottom  will  be 
forced  off  at  the  instant  the  surface  of  the  water  reaches  the  nut. 

§  63,  p.  80.  Specific  Gravity.  One  of  the  pans  of  the  bal- 
ances furnished  by  the  author  has  a  hook  beneath  it,  from  which 
specimens  are  suspended.  The  gram  weights  accompanying 
the  same  are  made  of  brass,  and  the  centimeter  and  millimeter 
weights  of  aluminum ;  and  the  whole  are  neatly  mounted  in  a 
block  of  wood. 


130  GENERAL  REVIEW   OF  PHYSICS. 

The  pupil  will  soon  discover  (However  simple  it  may  seem  to 
him  before  trial)  that  weighing  is  an  art  at  which  he  will  find 
himself  quite  awkward  at  first.  He  will  learn  it  better  by  expe- 
rience than  precept.  A  few  directions,  like  the  following,  will 
be  serviceable  to  him. 

Always  ascertain  the  weight  of  a  solid  in  air,  before  it  is  wet 
by  the  liquid. 

When  weighing  in  a  liquid,  see  that  the  solid  is  completely 
immersed,  and  nowhere  touches  the  vessel  holding  the  liquid. 

While  changing  the  weights,  hold  the  beam  with  one  hand, 
that  it  may  not  fall  from  its  support  and  suffer  injury. 

It  is  not  desirable  to  use  specimens  weighing  in  the  air  more 
than  from  5g  to  8s.  Specimens  even  lighter  than  these  will 
answer  just  as  well.  After  weighing  one  or  two  specimens, 
the  pupil  will  progress  very  rapidly,  will  be  delighted  with  the 
work,  and  should  be  allowed  to  use  as  many  specimens  as  time 
will  permit. 

§  74,  p.  98.  This  experiment  is  hardly  practicable,  but  its 
description  will  serve  to  indicate  to  the  pupil  the  true  method 
of  iinding  the  centre  of  gravity  of  a  mass. 

§  77,  p.  104.  The  plank,  Fig.  86,  should  have  a  shallow 
groove  cut  in  it,  to  guide  the  ball.  Teachers  report  very  sat- 
isfactory results  from  this  experiment. 

§  81,  p.  108.  "I  require  my  pupils  to  draw  the  paths  of 
projectiles  at  different  angles,  as  indicated  by  the  streams  of 
\vater  from  the  Eight-in-one  apparatus  with  the  tube  elevated 
at  different  angles,  and  have  obtained  good  results."  —  G.  F. 
FORBES,  Roxbury  Latin  School,  Boston. 

§  81,  p.  110.  Improved  Apparatus  for  verifying  the  Second 
Laiv  of  Motion.  The  rod  d,  Fig.  20,  is  drawn  back  toward 
the  left,  and  the  detent  pin  c  is  placed  in  one  of  the  three  slots. 
One  of  the  brass  balls  is  then  placed  on  the  projecting  rod,  and 
in  contact  with  the  end  of  the  instrument  as  at  A ;  the  other 
ball  is  placed  in  the  tube  B.  Release  the  detent,  and  the  ball 
at  7>,  struck  by  the  rod  d,  is  projected  with  a  force  (when  the 


CHAPTER   1 1.  —  DYNAMICS. 


139 


spring  is  under  its  greatest  strain)  of  about  15  Ibs.  At  the 
instant  it  escapes  the  end  of  tube  13,  and  is  free  to  fall,  the  rod 
leaves  ball  A,  and  the  latter  begins  to  fall.  Both  balls  are 
pierced  with  holes,  in  order  that  the  masses  of  both  may  be 
equal.  It  is  believed  that  this  apparatus  is  the  only  one  of  the 
kind  which  has  given  entire  satisfaction. 

Fig.  91,  p.  111.  For  the  pendulum  A  six  iron  balls  are  used, 
pierced  by  holes  through  their  centers,  through  which  a  string  is 
passed.  The  balls  are  kept  in  place  by  knots  tied  in  the  string. 

The  length  of  a  pendulum,  e.g.,  B,  is  approximately  the  dis' 
tance  from  the  point  of  suspension  to  the  center  of  the  bah1. 


Fig.  20. 

§  82,  p.  111.  The  center  of  oscillation  is  that  point  of  a 
pendulum  that  vibrates  in  the  same  time,  as  if  free  from  the 
influence  of  all  other  particles. 

§  88,  p.  119.  The  usual  mechanical  definition  of  work  is  here 
given.  A  complete  dynamical  definition,  of  course,  should  be 
made  to  include  negative  as  well  as  positive  work,  and  may  be 
stated  as  follows :  When  a  force  moves  a  body  against  resist- 
ance, or  alters  the  rate  of  motion  of  a  body,  it  is  said  to  do  work. 

§  92,  p.  121.  Potential  energy  —  energy  of  position  —  has 
been  called  energy  of  stress,  i.e.,  energy  due  to  stress.  It  is 
really  due  to  both  position  and  stress.  If  we  define  stress  pro- 


140  GENERAL   REVIEW   OF   PHYSICS. 

visionally  as  a  pressure  or  a  pull,  then  we  shall  find  that  pressure 
is  transformed  into  the  energy  of  motion  if  the  bodies  pressed 
upon  can  move,  i.e.-,  are  in  a  position  which  admits  of  motion. 

§  96,  p.  126.  The  erg  may  also  be  denned  as  the  work  done 
in  the  latitude  of  the  Northern  States  by  raising  -g-J-g-  of  a  gram- 
mass  to  the  hight  of  lcm.  The  objection  to  this  method  of 
definition  is  that  it  is  a  variable  measure.  The  same  may  be 
said  of  the  foot-pound,  which  also  evidently  varies  with  locality, 
and  must  be  reduced  at  each  place  to  absolute  units  by  the 
equation 

Work  =  Fs  =  weight  x  s  —  Mgs. 

For  example,  in  the  Northern  States  the  work  done  in  raising  a 
pound-mass  through  1  foot  is 

Mgs  =  1  X  32.2  x  1  =  32.2  foot-poundals. 

§  101,  p.  131.  Power.  The  pupil  should  be  informed  that, 
in  connection  with  machines,  the  term  power  has  a  technical 
signification  which  is  quite  distinct  from  its  usual  signification 
in  dynamics.  Here  it  is  used  in  the  sense  of  force. 

§  101,  p.  132.  Law  of  Machines.  In  a  perfect  machine  (i.e., 
one  in  which  no  internal  work  is  done)  the  work  done  upon  the 
machine  (  =  Fs)  is  equal  to  the  work  done  by  the  machine 
(  =  1^^)  ;  or,  Fs  =  JFjSj ;  hence,  F :  Fl : :  s  :  sx. 

P.  135.  Levers.  If  a  teacher  has  a  "  plenty  of  time"  (?) 
he  may  teach  the  popular  but  useless  division  of  levers  into 
three  classes. 


CHAPTER  III. 

HEAT. 

§  103,  p.  139.  When  the  water  in  this  experiment  nearly 
reaches  the  boiling-point,  it  will  be  forced  out  in  a  constant 
stream.  Previous  to  that,  it  will  only  escape  in  drops. 

§  110,  p.  142,  Exp.  4.  In  the  apparatus  prepared  especially 
for  this  experiment,  several  wires  of  different  metals  are  fastened 


CHAPTER   IIL  —  HEAT.  141 

upon  a  board,  and  made  to  converge  to  a  point  where  the  flame 
is  to  be  located.  By  running  the  fingers  along  the  several  wires 
toward  the  heated  end,  until  they  reach  the  point  in  each  where 
the  heat  is  unendurable,  and  noting  the  distance  of  these  points 
respectively  from  the  flame,  the  pupil  is  enabled  to  determine 
with  a  great  degree  of  accuracy  the  relative  conductivities  of 
the  several  metals.  He  will  notice  that  those  metals  which  are 
the  poorest  conductors  become  incandescent  first,  and  should 
be  required  to  explain  this  phenomenon. 

Exp.  5.  The  pupil  should  be  directed  carefully  to  avoid 
allowing  the  flame  to  touch  the  part  of  the  tube  not  covered 
by  the  water. 

§  111,  Exp.  1.  The  success  of  this  experiment  will  depend 
largely  upon  the  skill  in  manipulation,  and  had  better  be  per- 
formed by  the  teacher  only.  It  will  be  well  to  heat  the  water 
in  the  beaker  as  warm  as  can  be  borne  by  the  hands  before 
inserting  the  tube. 

§  112,  p.  145.  Ventilation.  "The  volume  of  air  to  be  re- 
newed in  places  requiring  to  be  purified  may  be  fixed  as 
follows :  — 

Per  hour  aud  per  individual. 
"  Hospitals : 

Ordinary  cases 60  to  70cbra 

Wounded  persons 100 

At  times  of  epidemics 150 

Prisons 50 

Workshops,  ordinary 60 

unhealthy 100 

Theatres,  music-halls,  etc 40 

Long  gatherings,  meetings 60 

Short  gatherings,  meetings 30 

Infant  schools '.  12  to  15 

Adult  schools 25  to  30 

Stables,  etc 180  to  200 

u  These  figures  agree  with  those  of  English,  American,  and 
German  hygienists."  —  GENERAL  MORTN,  Director  of  the  Con- 
se^vatoire  des  Arts  ct  Metiers,  at  Paris. 


142  GENERAL  REVIEW   OF  PHYSICS. 

§  127,  p.  158.  "Let  us  suppose  that  the  rarefaction  is  car- 
ried on  so  far  that  only  one  particle  out  of  every  original  million 
is  left  in  the  space  exhausted.  The  pressure  is  one-millionth 
of  its  original  amount ;  but  any  molecule  once  in  motion  has 
one-millionth  its  former  chance  of  encountering  any  other  mole- 
cule, and,  consequently,  its  average  free-path  is  magnified  a 
millionfold.  The  mean  path  would  then  be  (Crookes)  1 0  \  0  6mm 
X  1,000,000  =  100mm,  or  about  4  inches.  By  means  of  a  good 
Sprengel  pump,  exhaustion  to  the  hundred-millionth  of  an  at- 
mosphere can  be  attained,  and  the  mean  free-path  of  the  gas 
so  rarefied  would  be  about  33  feet.  In  our  atmosphere,  at  a 
bight  of  210  miles,  the  single  molecules  are  relatively  so  few 
(1000  to  the  ccm.)  that  each  molecule  might  travel  through 
a  uniform  atmosphere  of  that  density  for  60,000,000  miks 
without  entering  into  collision.  Beyond  a  hight  of  300  miles, 
the  atmosphere  is  so  rare  (less  than  one  molecule  per  cubic 
foot)  that  the  particles  might  freely  travel  through  such  an 
atmosphere  from  one  fixed  star  to  another."  —  DANIELL. 

§  116,  p.  150.  Other  examples  of  abnormal  expansion  and 
contraction  are  Rose's  fusible  metal,  iodide  of  silver,  and 
India  rubber.  See  "  Elementary  Treatise  on  Heat,"  by  Bal- 
four  Stewart,  4th  ed.,  p.  40. 

P.  159,  Exp.  3.  Inasmuch  as  the  water  first  receives  the 
heat,  and  then  communicates  it  to  the  ice,  it  is  not  possible 
to  prevent  the  water,  even  though  we  constantly  stir  it,  from 
becoming  warmer  than  the  ice.  But  the  temperature  of  the 
ice  will  not  rise  above  0°  C. 

P.  161.  Boiling  point.  "Dr.  Carnelly  finds  that  ice,  if 
heated  under  an  exceedingly  small  pressure,  may  be  rendered 
very  hot  (180°  C.),  and  will  volatilize  freely,  yet  without 
molting,  unless  the  pressure  be  allowed  to  exceed  a  certain 
low  maximum,  which  he  calls,  the  critical  pressure."  — 
DANIELL. 

§  129,  p.  162.  The  condenser  furnished  by  the  author  con- 
sists of  a  vessel  having  a  capacity  of  four  to  five  liters,  in 


CHAPTER  III.  —  HEAT.  143 

which  is  coiled  six  feet. of  pure  copper  tube.  The  glass  delivery 
tube  fr,  Fig.  115,  is  connected  with  one  end  of  this  copper  tube 
by  a  rubber  connector.  From  the  other  end  of  the  copper  tube 
which  pierces  the  vessel,  near  its  bottom,  escapes  the  distilled 
liquid.  Cold  water  is  siphoned  into  the  condenser,  as  in  the 
figure,  and  the  hetitcd  water  escapes  near  the  top  of  the  vessel 
through  a  delivery  tube  into  a  sink. 

§  130,  p.  163.  Molecular  Theory  of  Evaporation  and  Con- 
densation. "We  have  seen  that  in  the  case  of  a  gas,  some 
of  the  molecules  have  a  much  greater  velocity  than  others,  so 
that  it  is  only  to  the  average  velocity  of  all  the  molecules  that 
we  can  ascribe  a  definite  value.  It  is  probable  that  this  is  also 
true  of  the  motions  of  the  molecules  of  liquids,  so  that,  though 
the  average  velocity  may  be  much  smaller  than  in  the  vapor 
of  that  liquid,  some  of  the  molecules  in  the  liquid  may  have 
velocities  equal  to  or  greater  than  the  average  velocity  in  the 
vapor.  If  any  of  the  molecules  at  the  surface  of  the  liquid 
have  such  velocities,  and  if  they  are  moving  from  the  liquid, 
they  will  escape  from  those  forces  which  retain  the  other  mole- 
cules as  constituents  of  the  liquid,  and  will  fly  about  as  vapor 
in  the  space  outside  the  liquid.  This  is  the  molecular  theory  of 
evaporation.  At  the  same  time,  a  molecule  of  the  vapor  striking 
the  liquid  may  become  entangled  among  the  molecules  of  the 
liquid,  and  may  thus  become  part  of  the  liquid.  This  is  the 
molecular  explanation  of  condensation.  The  number  of  mole- 
cules which  pass  from  the  liquid  to  the  vapor  depends  on  the 
temperature  of  the  liquid.  The  number  of  molecules  which 
pass  from  the  vapor  to  the  liquid  depends  upon  the  density  of 
the  vapor  as  well  as  its  temperature.  If  the  temperature  of  the 
vapor  is  the  same  as  that  of  the  liquid,  evaporation  will  take 
place  as  long  as  more  molecules  are  evaporated  than  con- 
densed ;  but  when  the  density  of  the  vapor  has  increased  to 
such  a  value  that  as  man}'  molecules  are  condensed  as  evapo- 
rated, then  the  vapor  has  attained  its  maximum  density.  It  is 
then  said  to  be  saturated,  and  it  is  commonly  supposed  that 


144  GENERAL   HEVIEW   OF   PHYSICS. 

evaporation  ceases.  According  to  the  molecular  theory,  how- 
ever, evaporation  is  still  going  on  as  fast  as  ever ;  only,  con- 
densation is  also  going  on  at  an  equal  rate,  since  the  propor- 
tions of  liquid  and  of  gas  remain  unchanged."  —  MAXWELL. 

§  132,  p.  165,  Exp.  1.  For  obvious  reasons  the  results  here 
stated  are  theoretical  rather  than  practical,  inasmuch  as  the 
water  resulting  from  the  melting  ice  cannot  be  kept  at  the 
same  temperature  as  the  ice. 

More  satisfactory  results  may  be  obtained  by  pouring  lk  of 
water  at  80°  C.  upon  lk  of  ice  at  0°  C.,  and  noting  the  tempera- 
ture of  the  liquid  at  the  instant  the  ice  becomes  melted,  and 
calculating  from  the  data  found  the  number  of  units  of  heat 
rendered  latent. 

§  133,  p.  1G7.  Latent  heat.  "We  now  know  that  it  is  not 
heat  of  an}7  kind  ;  it  is  latent  or  potential  energy.  Work  must 
be  done  upon  ice  in  order  to  convert  it  into  the  more  highly- 
stressed  condition  of  water.  Water  differs  from  ice  at  the 
same  temperature  in  possessing  more  potential  energy."  — 
DANIELL. 

§  135,  p.  167.  The  reason  for  using  two  substances  in  this 
experiment  rather  than  one  is  that  a  given  quantity  of  water 
will  dissolve  more  of  both  than  of  either  alone  ;  consequently,  a 
greater  amount  of  heat  will  be  consumed. 

§  136,  p.  167,  Exp.  2.  For  the  purpose  of  comparison,  it 
would  be  well  to  take  water  at  about  60°  C.,  and  fill  the  porous 
cnp,  and  also  a  glass  beaker  of  as  nearly  the  same  size  and 
shape  as  practicable,  and  place  a  thermometer  in  each.  In  the 
course  of  five  to  ten  minutes  there  will  be  quite  a  perceptible 
change  in  the  temperature  of  the  two  bodies  of  liquid  which 
had  the  same  temperature  at  the  beginning. 

EXP.  3.  The  author  finds  that  raising  a  window  a  little  way, 
so  as  to  get  a  good  draft  of  air,  answers  much  better  than  the 
use  of  the  bellows.  It  ma}'  take  at  best  from  ten  to  fifteen 
minutes  to  freeze  the  water.  Hence,  it  would  be  well  to  reduce 


CHAPTER   III.  —  HEAT.  145 

the  temperature  of  the  water  to  a  low  point  by  means  of  a  freez- 
ing mixture  before  introducing  it  into  the  tube. 

§  145,  p.  174.  The  phrase  "  conservation  of  force"  is  some- 
times used,  but  should  be  avoided,  because  it  is  entirely  erro- 
neous. A  single  illustration  will  make  this  apparent.  Take  a 
lever  12  ft.  long,  place  the  fulcrum  3  ft.  from  one  end,  and 
apply  a  force  of  3  Ibs.  at  the  extremity  of  the  long  arm,  and  a 
force  of  9  Ibs.  will  be  exerted  at  the  other  end  of  the  lever. 
Here  force  is  apparently  created.  If  the  force  is  applied  at  the 
extremity  of  the  short  arm,  force  apparently  disappears.  But 
though  there  is  no  conservation  of  force,  there  is  a  strict  con- 
servation of  energy  in  this  and  in  all  other  mechanical  contri- 
vances. On  this  principle  is  to  be  explained  the  paradox  in 
the  statement  that  a  single-inch  piston  of  the  hydraulic  press, 
pressed  in  with  a  force  of  60  Ibs.,  will  commensurate  a  pressure 
of  60  Ibs.  to  every  square  inch  of  a  cylinder,  however  large. 

You  can  store  energy,  but  you  cannot  store  force  any  more 
than  3'ou  can  store  time.  A  stone  resting  on  the  ground 
presses  the  ground :  force  is  all  the  time  exerted,  but  the 
cleverest  engineer  could  not  drive  a  machine  b}T  using  a  weight 
resting  on  the  ground. 

§  147,  p.  175.  Joule's  Equivalent.  According  to  Joule's 
revision  of  this  physical  constant,  its  value  is,  at  sea-level  at 
the  latitude  of  Greenwich,  772.55  ft.  Ibs.  In  accordance  with 
tlrs  value,  the  calorie  =  423.985kgm  =  41,593,010,000  ergs. 

If  the  numerical  value  is  so  chosen  as  to  give  the  work  corre- 
sponding to  a  unit  of  heat,  it  is  called  Joule's  Equivalent,  or  the 
mechanical  equivalent  of  heat ;  if,  on  the  contrary,  it  gives  the 
heat  corresponding  to  a  unit  of  work,  it  is  called  the  thermal 
equivalent  of  work.  If  the  former  is  denoted  by  J,  the  latter  is 

-  = =0.00235  calorie  ;  i.e.,  lksm  of  work  is  equivalent 

J     423.985 

to  0.00235  calorie  of  heat. 


146  GENERAL   REVIEW    OF   PHYSICS. 

CHAPTER   IV. 

ELECTRICITY. 

§  151,  p.  181.  Current.  Electricity,  whatever  it  is,  can  pass 
from  one  body  to  another  only  by  passing  consecutively  through 
every  point  of  the  path  joining  them.  We  may,  therefore,  with 
perfect  propriety  speak  of  a  current  of  electricity. 

§  158,  p.  184.  "  How  Electricity  Originates."  In  the  first 
edition  of  the  Physics  the  foregoing  expression,  as  well  as  the 
expression  "  generate  electricity,"  were  inadvertently  used. 
These  expressions,  though  often  convenient,  ought  carefully 
to  be  avoided,  as  they  convey  erroneous  ideas.  Electricity  is 
a  something  whose  sum  total  in  the  universe  seems  to  be  con- 
stant, for  we  cannot  alter  the  quantity  contained  in  an  isolated 
space  by  any  method.  We  conclude  that  electricity  is  inde- 
structible and  uncreatable,  by  an  exact  parity  of  reasoning  with 
that  by  which  we  are  convinced  that  matter  is  indestructible  and 
uncreatable. 

When  a  body  is  electrified,  another  is  always  charged  with  an 
equal  amount  of  the  opposite  kind  of  electricity,  so  that  we  may 
regard  the  process  as,  not  the  generation  of  anything,  but  a 
separation. 

Exp.  4,  p.  194.  A  suitable  battery  for  this  experiment  con- 
sists of  two  Bunsen  cells  connected  tandem.  The  electrolyte 
may  be  composed  of  sulphuric  acid  diluted  with  twenty  times 
its  volume  of  water. 

§  178,  p.  203.  "  The  resistance  of  all  wires  increases  as  the 
temperature  rises,  and  the  resistance  of  nearly  all  metals  in- 
creases at  the  same  rate,  iron  and  thallium,  according  to  Dr. 
Matthiesen,  being  the  only  exceptions.  From  the  tables  given 
by  Latimer  Clark  we  learn  that  the  resistance  of  iron  wire  in- 
creases about  thirty-five  hundrcdths  (0.35)  per  cent  for  each 
degree  Fahrenheit,  and  that  the  resistance  of  copper  increases, 


CHAPTER    IV.  —  ELECTRICITY.  147 

as  the  temperature  rises,  twenty-one  hundredths  (0.21)  per  cent 
for  each  degree. 

4 '  The  rate  of  increase  is  not  reckoned  all  through  on  the  origi- 
nal resistance,  but  is  computed  in  the  same  manner  as  compound 
interest  on  a  sum  of  money.  For  example,  if  we  have  a  wire 
which  measures  100  ohms  at  60°  F.,  and  the  resistance  be  in- 
creased a  certain  amount  by  a  rise  of  one  degree  in  temperature, 
it  will  be  increased  by  the  next  degree  of  rise  at  the  same  rate 
per  cent,  calculated  on  the  original  resistance,  plus  the  amount 
increased  by  the  first  degree  of  rise."  —  LOCKWOOD. 

Exp.  1,  p.  215.  As  many  as  four  Bunsen  cells,  connected 
abreast,  should  be  used  in  this  experiment,  and  the  extremities 
of  the  wires  should  not  dip  more  than  lmm  into  the  mercury. 
In  using  the  apparatus  illustrated  in  Fig.  152,  a  very  strong 
current  will  be  required. 

Exp.  2,  p.  21G.  In  the  apparatus  furnished  by  the  author  for 
this  experiment,  zinc  and  carbon  plates  are  used,  and  a  solution 
of  bichromate  of  potash,  like  that  used  in  a  Grenet  cell,  should 
be  used  in  this  floating  battery.  The  battery,  left  to  itself,  will 
take  up  a  position  with  its  coil  N  and  S. 

§  190,  p.  218.  Ampere's  theory  serves  a  very  useful  purpose 
in  acquainting  the  pupil  with  very  many  phenomena  of  elec- 
tricity and  magnetism,  and  the  laws  governing  them,  very  much 
as  the  fluid  theor}T  of  electricity  has,  at  least,  furnished  a  very 
convenient  language  in  which  to  express  the  various  electrical 
phenomena.  Yet,  plausible  as  this  theory  seems  in  many  of 
its  aspects,  it  is  open  to  many  serious  objections,  of  which  we 
give  only  one.  It  would  seem  that,  if  this  theory  be  true,  force 
would  be  required  to  demagnetize  instead  of  to  magnetize  mat- 
ter ;  for,  if  the  assumed  molecular  currents  forming  an  inhe- 
rent part  of  the  constitution  of  matter  really  exist,  they  must, 
by  the  fundamental  laws  of  electric  currents,  always  arrange 
themselves  in  parallel  order. 

Exp.  3,  p.  221.  In  performing  this  experiment,  the  glass 
plate  should  be  thin,  and  should  not  touch  the  steel  disk.  It 


148  GENERAL   REVIEW    OF   PHYSICS. 

would  be  well  to  have  a  glass  plate  set  in  a  wooden  frame  for 
this  purpose. 

§  192,  p.  222.  Magnetic  Poles  of  the  Earth,  and  Vari- 
ation of  the  Needle.  "  When  the  phenomena  of  terrestrial 
magnetism  were  first  somewhat  accurately  observed,  about  300 
years  ago,  the  needle  pointed  here  in  England  a  little  to  the 
east  of  north.  A  few  years  later  it  pointed  due  north ;  then, 
until  about  the  year  1820,  it  went  to  the  west  of  north,  and 
now  it  is  coming  back  towards  the  north.  .  .  .  Everything 
goes  on  as  if  the  earth  had  a  magnetic  pole  revolving  at  a 
distance  of  about  twenty  degrees  round  the  true  North  Pole. 
.  .  .  About  200  years  from  now  we  may  expect  the  magnetic 
pole  to  be  between  England  and  the  North  Pole  ;  and  in  Eng- 
land at  that  time  the  needle  will  point  due  north,  and  the  dip  will 
be  greater  than  it  has  been  for  1000  years,  or  will  be  again  for 
another.  That  motion  of  the  magnetic  pole  in  a  circle  round  the 
true  North  Pole  has  already,  within  the  period  during  which  accu- 
rate measurements  have  been  made,  extended  to  somewhat  more 
than  a  quarter  of  the  whole  revolution."  — SIR  WILLIAM  THOMSON. 

§  207,  p.  237.  The  principal  source  of  difference  of  potential 
is  the  contact  of  dissimilar  surfaces,  —  that  is,  either  of  differ- 
ent substances,  or  of  two  pieces  of  the  same  substance  whose 
surfaces  are  in  different  conditions.  A  piece  of  rosin  and  a 
piece  of  glass  will,  after  contact,  be  more  difficult  to  pull 
asunder  than  two  pieces  of  rosin  or  two  pieces  of  glass  ;  and 
if  they  be  rubbed  together,  so  as  to  multiply  the  points  of  con- 
tact, the  effect  is  multiplied.  When  pulled  asunder,  two  such 
bodies  are  found  to  be  charged  equally  and  oppositely  :  across 
the  surface  of  contact  there  has  been  a  separation  of  positive 
from  negative  electricity.  The  development  of  electrical  con- 
dition is  thus  necessarily  a  phenomenon  of  continual  recurrence, 
and  it  greatly  influences  the  adhesion  of  one  body  to  another. 
In  all  probability,  wherever  there  is  friction,  the  energy  ulti- 
mately converted  into  heat  is,  in  the  first  place,  converted  into 
the  energy  of  electrical  separation. 


CHAPTER   IV.  —  ELECTRICITY.  149 

"  When  two  substances  have  different  molecular  velocities  at 
their  common  surface  of  mutual  contact,  the  molecules  hamper 
one  another,  and  energy  is  lost :  this  energy  takes  the  form  of 
the  energy  of  electrical  displacement."  —  DANIELL. 

§  233,  p.  250.  The  quickest  way  to  charge  a  battery  of  jars 
is  to  connect  the  inner  coatings  with  one  of  the  conductors  of 
the  electrical  machine,  and  the  outer  coatings  with  the  other 
conductor.  Likewise,  in  using  the  Aurora  tube,  the  top  of  the 
tube  should  be  connected  with  one  conductor  and  the  bottom  of 
the  tube  with  the  other.  And  the  same  is  true  of  all  other 
pieces  of  apparatus  through  which  charges  of  electricity  are  to 
be  sent. 

Fig.  192,  p.  254.  A  good  substitute  for  the  apparatus  here 
described  may  be  easily  and  cheaply  prepared  as  follows : 
Apply  a  varnish,  made  b}*  dissolving  gum  shellac  in  alcohol,  to 
one  side  of  a  piece  of  window-glass  about  6  inches  long  and  4 
inches  wide,  and  sift  iron  filings  over  the  wet  surface.  As  the 
alcohol  evaporates,  the  gum  will  cause  the  filings  to  adhere  firmly 
to  the  glass.  The  glass  thus  prepared  may  be  used  in  the 
manner  directed  for  the  mica  disk. 

A  piece  of  common  mirror-glass  also  answers  this  purpose 
well. 

§  230,  p.  256.  Great  E.M.F.  is  produced  in  every  frictional 
machine,  but  it  is  an  essential  part  of  the  contrivance  that  the 
rubber  and  the  main  conductor  shall  be  separated  by  the  insu- 
lator which  is  rubbed.  We  cannot,  therefore,  even  if  we  con- 
nect the  rubbers  with  the  main  conductor,  complete  a  circuit, 
except  through  this  insulator.  Now  this  insulator  has  such  an 
enormous  resistance  that,  according  to  Ohm's  Law,  even  the 
great  E.M.F.  produced  by  the  machine  can  produce  only  a  very 
feeble  current. 

§  234,  p.  259.  Voltaic  Arc.  One  may  form  a  good  idea  of 
the  size  and  shape  of  the  arc  "by  looking  at  it  through  a  colored 
or  smoked  glass. 

§  245,  p.  2G9.     The  following  very  clear  and  concise  descrip- 


150  GENERAL   REVIEW    OF   PHYSICS. 

tion  of  the  operation  of   the  telephone  is  taken,   with  slight 
modification,  from  Jenkins's  "Manual  of  Electricity":  — 

' '  One  instrument,  which  shall  be  called  the  receiver,  is  held 
to  the  ear.  The  person  wishing  to  send  a  message  speaks  into 
the  mouthpiece  of  the  other  instrument,  which  will  be  called  the 
sender.  The  spoken  words  cause  the  air  to  vibrate  in  front  of 
the  sender,  and  the  disk  E  of  that  instrument  vibrates  as  the 
air  does,  alternately  approaching  and  leaving  the  end  of  the 
magnet  M.  Each  change  in  the  position  of  the  disk  E  causes 
a  change  in  its  magnetism,  and  in  the  magnetic  field  occupied 
by  the  coil  B.  Each  change  in  the  magnetic  field  causes  an 
induced  current  in  the  circuit.  This  current  is  reversed  at  each 
change  of  direction  in  the  motion  of  the  disk,  and,  moreover, 
its  magnitude  is  at  each  instant  sensibly  proportional  to  the  rate 
at  which  the  disk  E  is  moving ;  for  we  know  that  the  induced 
current  is  proportional  to  the  rate  of  change  in  the  field  enclosed 
by  the  coil  J3,  and  we  see  that  this  rate  of  change  will  depend 
on  the  rate  at  which  the  disk  E  is  moving.  The  induced  cur- 
rents acting  on  the  receiving  instrument  will  change  the  mag- 
netism of  the  steel  magnet  A  and  the  magnetic  field  in  which 
the  disk  E  of  the  receiver  lies  ;  each  change  will  be  accompanied 
by  a  change  in  the  attraction  of  the  iron  disk  to  the  magnet,  and 
thus  the  disk  E  will  be  set  in  vibration.  It  will  move  to  and 
fro  as  often  as  the  direction  of  the  current  in  the  circuit  is 
reversed  ;  but,  more  than  this,  its  rate  of  motion  at  each  instant 
will  be  proportional  to  the  rate  of  change  in  the  magnetic  field 
it  occupies.  Now,  this  rate  of  change  is  the  same  rate  as  that 
of  the  change  in  the  current,  which  again  is  the  same  rate  as 
that  of  the  motion  of  the  sending  disk  E.  The  motions  of  the 
sending  and  receiving  disks  will  therefore  be  similar,  though  of 
unequal  magnitude.  The  air,  therefore,  in  front  of  them  — 
which  in  one  case  moves  the  disk,  and  in  the  other  is  moved  by 
it  —  will  also  vibrate  in  the  same  way  ;  and,  since  the  vibrations 
of  the  air  at  the  sending  end  produced  the  impression  of  articu- 
late words  on  the  ear,  so  the  vibrations  of  the  air  caused  by  the 


CHAPTER   V.  —  SOUND.  151 

disk  E  at  the  receiving  end  will  also  produce  the  impression  of 
the  same  articulate  sounds.  The  chief  difference  between  the 
two  sounds  is  one  of  magnitude.  The  action  of  the  two  disks 
is  similar  to  that  in  the  toy  telegraph,  where  -two  parchment 
disks  are  mechanically  connected  by  a  tight  string.  The  elec- 
trical currents  due  to  induction  give  those  impulses  in  the  one 
case  which  in  the  other  are  given  mechanically  by  the  string." 


CHAPTER  V. 

SOUND. 

§  267,  p.  288.  Loudness  of  Sound.  "The  sensible  loudness 
of  sounds  does  not  coincide  very  closely  with  their  physical  in- 
tensity. This  arises  partly  from  modification  in  the  form  of 
the  vibration  induced  by  so  complicated  a  transmission  through 
the  auditory  apparatus,  partly  from  causes  purely  physiolog- 
ical."—  DANIELL. 

§  274,  p.  294.  Very  fair  results  may  be  obtained  in  these 
experiments  with  an  ordinary  tuning-fork.  The  forks  mounted 
on  resonance-boxes  are  considerably  larger  and  more  expensive 
than  the  ordinary  tuning-fork,  and  are  usually  called  diapasons. 
They  should  be  set  in  vibration  by  bowing  with  a  large  bass 
bow,  the  bow  having  been  previously  rubbed  over  a  piece  of 
warm  rosin.  Avoid  striking  them  upon  hard  substances,  as 
permanent  injury  may  be  done  them  in  this  way.  Another  con- 
venient way  of  setting  them  in  vibration  is  by  drawing  quickly 
between  the  tines  a  rod  of  wood  whose  diameter  is  a  little  greater 
than  the  width  of  the  space  between  the  tines  at  their  extremities. 
Diapasons  should  be  carefully  protected  from  rust,  as  this  will 
alter  their  pitch.  Diapasons  like  those  in  Fig.  214  require 
especial  care,  as  a  very  little  rust,  or  a  very  slight  change  in 


152  GENERAL   REVIEW    OF   PHYSICS. 

the  elasticity  of  either  one,  may  alter  by  a  single  vibration,  or  a 
part  of  a  vibration,  the  vibration  rate  of  one  of  them.  In  that 
case  they  must  be  tuned  in  unison  by  an  experienced  hand  be- 
fore they  will  answer  again  the  purpose  of  showing  sympathetic 
vibrations.  To  protect  forks  from  rust,  previous  to  laying  away 
after  use,  they  should  be  wiped  with  a  woollen  cloth  slightly 
moistened  with  vaseline.  Vaseline  may  be  used  to  advantage 
to  protect  all  pieces  of  apparatus  made  of  iron  or  steel  from 
rust. 

§  296,  p.  321.  The  lowest  sound  is  obtained  by  touching  the 
center  of  one  side  and  bowing  the  corner.  The  damping  is  best 
done  by  touching  the  plate  with  the  extremity  of  the  finger-nail. 
A  node  is  always  started  from  the  point  that  is  touched,  while, 
of  course,  the  point  bowed  is  a  ventral  segment.  The  next 
note,  a  fifth  above,  is  produced  by  damping  the  corner  and 
bowing  the  center.  By  altering  the  position  of  the  finger  and 
bow,  and  sometimes  using  finger  and  thumb,  a  great  variety  of 
figures  may  be  obtained,  which  may  be  further  extended  by 
changing  the  points  of  support. 

If  sand  (fine  writing  sand  is  best)  mixed  with  lycopodium 
powder  is  strewed  upon  a  vibrating  plate,  the  sand  will  collect 
on  the  nodal  lines  ;  but  the  lycopodium,  by  the  agitation  of  the 
air,  will  be  blown  toward  the  center  of  each  vibrating  segment. 


CHAPTER  VI. 
LIGHT. 

§  300,  p.  325.  Kinds  of  Radiation.  "When  a  succession 
of  waves  impinges  on  a  mass  of  ordinary  matter,  the  effect  varies 
according  to  the  nature  and  the  condition  of  the  body  which  re- 
ceives their  shock  ;  if  it  be  an  ordinary  opaque  mass,  that  mass 


CHAPTER   VI. LIGHT.  153 

may  be  warmed,  wave-motion  being  transformed  into  heat,  and 
the  waves,  which  have  impinged  upon  it,  are  ex  post  facto  called 
a  beam  of  radiant  heat ;  if  they  fall  upon  the  eye,  they  may  pro- 
duce a  sensation  of  light,  and  the  wave  system  is  then  called  a 
beam  of  light ;  falling  upon  a  sensitized  photographic  plate,  or  a 
living  green  leaf,  it  may  operate  chemical  decomposition,  and 
it  is  then  called  a  beam  of  actinic  rays.  The  word  "  rays"  in 
the  last  phrase  may  be  understood  to  mean,  not  imaginary  lines 
at  right  angles  to  the  wave-front,  but  kinds  of  radiation ;  and 
hence  we  speak  of  heat  rays,  of  light  rays,  of  chemical  or  ac- 
tinic rays,  these  names  being  given  to  one  and  the  same  train 
of  waves  according  to  the  effects  which  it  is  found  competent  to 
produce.  But  while  ether-waves  are  in  course  of  traversing  the 
ether,  there  is  neither  heat,  light,  nor  chemical  decomposition ; 
merely  wave-motion  and  transf  erence  of  energy  by  wave-motion. 
Hence,  none  of  these  names  can  in  strictness  be  applied  to  a 
train  of  waves  while  these  are  actually  travelling  through  the 
ether. 

"According  to  Clerk  Maxwell's  view,  the  ether  is  a  homo- 
geneous body,  a  non-conductor  of  electricity.  Periodic  electric- 
stresses  applied  to  this  produce  waves  which  travel  at  the  rate 
of  about  300,000,000  meters  per  second.  These  waves  are 
waves  of  transverse  vibration,  and  there  is  no  vibration  longi- 
tudinal or  normal  to  the  wave-front."  —  DANIELL. 

§  311,  p.  334.  In  a  course  of  lectures  given  at  the  Lowell 
Institute  in  Boston,  in  1882,  Prof.  S.  P.  Langle}T  said  that 
the  light  of  the  sun  is  two  and  a  half  times  as  brilliant  as  the 
same  area  of  electric  (arc)  light ;  and  that  if  a  calcium  light  be 
held  between  the  eye  and  the  sun,  the  light  would  appear  to  be 
a  black  spot  upon  the  sun.  As  a  measure  of  comparison,  in 
assisting  the  comprehension  of  the  infinite  quantity  of  light 
thrown  off  by  the  sun,  he  remarked  that  if  there  was  an  electric 
light  of  2000  candle  power  on  each  square  foot  of  the  surface  of 
the  earth,  then  the  whole  light  from  the  earth  would  be  less  than 
one-billionth  that  from  the  sun. 


154  GENERAL   EEVIEW   OF   PHYSICS. 

§  301,  p.  326.  "We  are  led  to  infer,  therefore,  that  there  is 
such  a  medium,  which  we  call  the  luminffcrous  ether,  or  simply 
the  ether ;  that  it  can  convey  energy ;  that  it  can  present  it  at 
any  instant,  partly  in  the  form  of  kinetic,  partly  in  that  of 
potential  energy ;  that  it  is,  therefore,  capable  of  displacement 
and  of  tension ;  and  that  it  must  have  rigidity  and  elasticity. 
Calculation  leads  us  to  infer  that  its  density  is  (Clerk  Maxwell) 
i  ooo  ooo  000,000,000,000.000  that  °f  water,  or  equal  to  that  of  our  atmos- 
phere at  a  hight  of  about  210  miles,  a  density  vastly  greater 
than  that  of  the  same  atmosphere  in  the  interstellar  spaces  ; 
that  its  rigidity  is  about  1)0oo,ooo,ooo  tnat  °^  stee^ '»  nence?  that  it 
is  easily  displaceable  by  a  moving  mass  ;  that  it  is  not  discon- 
tinuous or  granular ;  and  hence,  that,  as  a  whole,  it  may  be 
compared  to  an  impalpable  and  all-pervading  jelly,  through 
which  light  and  heat  waves  are  constantly  throbbing,  which  is 
constantly  being  set  in  local  strains  and  released  from  them, 
and  being  whirled  in  local  vortices,  thus  producing  the  various 
phenomena  of  electricity  and  magnetism ;  and  through  which 
the  particles  of  ordinary  matter  move  freely,  encountering  but 
little  retardation  if  any ;  for  its  elasticity,  as  it  closes  up  behind 
each  moving  particle,  is  approximately  perfect."  —  DANIELL. 

' '  We  are  at  liberty  to  deny  the  existence  of  all  action  at  a 
distance,  and  attribute  it  to  the  intervening  medium,  which,  to 
be  logical,  we  must  assume  to  be  continuous  and  not  molecular 
in  constitution."  — ROWLAND. 

"It  is  a  most  wonderful  fact  that  we  have  never  been  able 
to  discover  anything  on  the  earth  by  which  our  motion  through 
a  medium  can  be  directly  proved.  Carried,  as  we  suppose,  by 
the  earth  with  immense  velocity  through  the  regions  of  space 
filled  with  ether,  we  have  never  yet  been  able  to  prove  any 
direct  influence  from  this  ethereal  wind."  —  ROWLAND. 

§  344,  p.  373.  "  The  bolometer,  a  curious  instrument  recently 
introduced  by  Prof.  S.  P.  Langley  for  measuring  minute  quanti- 
ties of  radiant  energy,  promises  important  results  in  optical 
and  astronomical  investigations.  It  is  based  upon  the  fact 


CHAPTER    VI.  —  LIGHT.  155 

that,  when  equal  conductors  of  the  electrical  current  are  at  the 
same  temperature,  their  conductivities  are  equal,  and  the  current 
of  a  battery  can  be  equally  divided  between  them ;  while,  if 
unequal!}-  heated,  their  conductivities  are  unequal,  and  the  dif- 
ference in  current  can  be  detected  with  the  galvanometer.  By 
substituting  thin  sheets  of  metal  for  the  wires  ordinarily  em- 
ployed as  conductors,  so  as  to  take  up  and  part  with  its  radia- 
tions with  great  rapidity,  an  instrument  is  produced  capable  of 
measuring  such  minute  quantities  of  heat  as  0.00001°  C.  ; 
capable,  also,  of  recording  the  infinitesimal  heat  radiations  of 
the  diffraction  spectrum.  The  interesting  statement  is  made  in 
this  connection,  that  the  curves  of  light,  heat,  and  actinism, 
instead  of  receding  from  each  other,  as  commonly  understood, 
are  in  reality  coincident,  that  is,  the  solar  beam,  instead  of  con- 
sisting of  a  pencil  of  rays  bound  into  a  luminous  sheaf  called 
light,  is  a  homogeneous  and  simple  energy,  the  names  light,  heat, 
and  actinism  being  merely  names  for  its  different  modes."  — 
ELECTRICIAN. 

§  346,  p.  375.  Effect  of  the  Atmosphere  on  the  Color  of  Sun- 
light. "  Sunlight  is  originally  bright  blue,  and  is  extremely  rich 
in  the  more  refrangible  rays,  but  filtration  through  two  absorbent 
atmospheres  —  that  of  the  sun  and  that  of  the  earth  —  renders  it 
a  yellowish  white."  —  LANGLEY. 

§  347,  p.  378.  It  is  now  the  received  view  that  all  color- 
perceptions,  infinite  as  they  may  be  in  intensity  and  in  hue,  are 
due  to  the  simultaneous  excitation  of  three  sets  of  nerve-ends 
by  stimuli  of  relatively  varying  amount.  These  three  physio- 
logically-primary color  sensations  are  (Young  and  Helmholtz) 
red,  green,  and  violet.  When  orange  light  affects  the  eye,  the 
nerve-ends  sensitive  to  red  are  affected  ;  those  sensitive  to  green 
are  affected,  but  less  so,  while  those  sensitive  to  violet  are  very 
feebly  affected.  When  the  red  and  green  nerve-ends  (as  we 
may  for  convenience  call  them)  are  equally  affected,  the  resultant 
impression  is  one  of  yellow  ;  hence,  a  mixture  of  red  light  with 
green  light  produces  a  sensation  of  yellow.  In  like  manner,  the 


156  GENERAL    REVIEW   OF   PHYSICS. 

mixture  of  green  and  violet  in  varying  proportions  may  produce 
all  the  color-sensations  which  the  spectrum  between  the  green 
and  violet  is  capable  of  stimulating,  as  may  be  shown  by  the 
rotation  of  suitable  color-disks. 

§  351,  p.  379.  Interference.  "  The  twinkling  of  stars  is 
another  effect  of  interference :  light  coming  to  the  eye  from  a 
star,  so  distant  as  to  be  practically  a  single  luminous  point, 
arrives  in  rays  which  have  traversed  slightly  unequal  distances 
in  an  irregularly  refracting  atmosphere,  and  thus  enter  the  eye  in 
unequal  phases.  Now  one  color  is  distinguished,  now  another ; 
the  eye  perceives  colored  light  complementary  to  that  momentarily 
lost.  No  two  persons  can,  as  a  rule,  see  any  star  twinkling  in 
precisely  the  same  manner.  The  planets  twinkle  only  at  their 
edges  ;  their  disks  present  many  points  or  sources  of  light,  whose 
scintillations,  on  the  whole,  mask  one  another."  —  DANIELL. 

§  353,  p.  384.  Polarization.  "  Ordinary  light  consists  of 
vibrations  taking  place  always  in  planes  at  right  angles  to  the 
direction  of  the  ray,  but  in  all  directions  in  those  planes.  That 
is,  if  the  ray  travels  along  the  axle  of  a  wheel,  the  vibrations 
composing  it  are  all  in  the  plane  of  the  wheel,  but  are  executed 
along  any  or  all  of  the  spokes. 

44  The  effect  of  reflecting  light  at  certain  angles  from  cer- 
tain substances,  or  of  passing  it  through  certain  crystalline 
substances,  is  to  cause  all  the  vibrations  to  take  place  in  the 
same  direction,  —  that  is,  along  one  spoke  of  the  wheel  and  the 
spoke  opposite  to  it. 

"  The  light  is  then  said  to  be  polarized.  Now,  if  the  wheel, 
without  being  rotated,  be  slid  along  the  axle,  the  spoke  along 
which  the  vibrations  take  place  will  trace  out  a  plane. 

; '  When  no  rotative  force  is  applied  to  the  polarized  light,  the 
vibrations  all  take  place  in  this  plane,  and  the  light  is  said  to  be 
1  plane-polarized.' 

"  We  cannot  detect  by  the  eye  in  what  plane  light  is  polarized, 
or,  indeed,  whether  or  not  it  is  polarized  at  all.  In  order  to  do 
so,  we  have  to  take  advantage  of  the  following  natural  law  :  — 


CHAPTEll    VI. — LIGHT.  157 

"Transparent  bodies  which  have  the  power  of  polarizing  light 
in  any  given  plane  are  opaque  to  light  already  polarized  in  a 
plane  at  right  angles  to  that  plane  ;  and  reflecting  surfaces  which 
have  the  power  of  polarizing  light  in  a  given  plane  will  not  reflect 
light  which,  when  it  falls  on  them,  is  already  polarized  in  a  plane 
at  right  angles  to  that  plane. 

"  Thus,  to  determine  in  what  plane  light  is  polarized,  we  have 
only  to  take  a  crystal  which  has  the  power  of  polarizing  light  in 
a  certain  plane,  fixed  with  regard  to  its  axis,  and  to  turn  it  round 
till  the  light  is  extinguished. 

' '  We  then  know  that  the  light  is  polarized  in  a  plane  at  right 
angles  to  that  plane  in  the  crystal."  —  GORDON. 

§  356,  p.  387.  "Whatever  light  is,  at  each  point  of  space 
there  is  something  going  on,  whether  displacement,  or  rotation, 
or  something  not  yet  imagined,  but  which  is  certainly  of  the 
nature  of  a  directed  quantity,  the  direction  of  which  is  normal 
to  the  direction  of  the  ray.  This  is  completely  proved  by  the 
phenomena  of  interference. "  —  MAXWELL. 


PART   IV. 


TEST    QUESTIONS. 

1 .  Describe  an  experiment  which  you  have  performed  at  your 
home,  and  state  the  lesson  derived  from  it. 

2.  Why,  as  you  raise  the  vessel  JB,  Fig.  22,  Physics,  higher 
and  higher,  is  the  rubber  forced  inward  more  and  more? 

3.  Name  some  phenomena  which  are  the  result  of  the  earth's 
attracting  the  moon  and  the  moon's  attracting  the  earth. — Ans. 
The  former  attraction  mainly  keeps  the  moon  in  her  orbit,  and 
the  latter  is  one  of  the  causes  of  tidal  phenomena. 

4.  What  is  the  distinction  between  mass  and  weight?    Which 
better  defines  a  body  ?     Why  ? 

5.  If  the  earth  were  a  homogeneous  shell  devoid  of  air,  and 
a  person  were  to  jump  from  one  side  toward  the  center,  where 
would  he  stop  ?     Could  he  stop  at  the  center  ?     Would  his  path 
be  straight  or  curved  ?     Would  his  motion  be  accelerated,  re- 
tarded, or  uniform  ?     What  would  be  the  effect  produced  upon 
the  earth  at  the  instant  he  jumps?     If  the  earth  and  his  body 
were  perfectly  elastic  (i.e.,  the  coefficient  of  restitution  =  1), 
how  long  would  he  continue  to  move  ?    If  in  his  journey  through 
the  hollow  space  he  should  let  drop  a  ball,  what  would  become 
of  it? 

6.  If  the  earth  were  a  homogeneous  sphere,  and  a  hole  ex- 
tended from  surface  to  surface  through  the  center,  and  the  hole 
were  a  vacuum,  and  a  ball  should  be  dropped  into  it,  where  would 
it  stop  ?    Where  would  it  have  its  maximum  velocity  ?    How 
long  would  it  continue  to  move  ? 


TEST   QUESTIONS. 

7.  A  coil  of  glass  tubing,  after  being  suspended  for  a  year, 
became  permanently  stretched.     What  property  does  this  phe- 
nomenon show  that  glass  possesses  ? 

8.  One  man  holds  one  end  of  a  rope  in  his  hands,  and  another 
man  pulls  the  other  end  of  the  rope  with  a  force  of  90  Ibs. 
What  force  does  the  latter  compel  the  former  to  exert  in  order 
to  retain  the  rope  in  his  hands  ?  —  Ans.    90  Ibs. 

9.  Two  men  at  opposite  extremities  of  a  rope  pull  each  with 
a  force  of  100  Ibs.     What  is  the  force  exerted  between  them  or 
the  tension  of  the  rope  ?  —  Ans.    100  Ibs. 

10.  What  force  is  necessary  to  separate  a  pair  of  Magdeburg 
hemispheres  from  which  the  air  has  been  entirely  exhausted,  and 
whose  diameter  is  five  inches?  —  Ans.    294.5  Ibs. 

11.  What  force   would  be  necessar}-  to  separate  the  above 
hemispheres  at  a  place  where  the  barometrical  column  is  20 
inches?  —  Ans.   196.3  Ibs. 

12.  What  force  would  be  necessary  to  separate  the   same 
hemispheres  at  sea-level  if  only  one-fourth  of  the  air  has  been 
removed  from  them?  —  Ans.   73.8  Ibs. 

13.  A  stone  weighing  a  kilo  rests  upon  a  shelf,  and  another 
stone  of  the  same  weight  is  suspended  by  a  string.    What  effect 
is  produced  by  the  force  of  gravity  acting  on  each?  —  Ans.    In 
the  former  case,  pressure  ;  in  the  latter,  tension. 

14.  If  the  shelf  is  removed  and  the  string  is  cut,  what  change 
in  the  effects  of  gravity  will  occur  ?  —  Ans.    Pressure  and  ten- 
sion will  cease,  and  motion  will  be  produced. 

15.  In  the  experiment  with  vessel  J5,  Fig.  22,  why  is  the 
rubber  pressed  in  farther  the  higher  the  vessel  is  raised  ?     Is  it 
because  the  pressure  of  the  air  increases  as  the  vessel  is  raised  ? 

— *16.  A  cubical  vessel,  whose  interior  dimension  is  6cm,  is  filled 
with  water  and  sits  upon  a  table.  What  is  the  entire  pressure 
exerted  by  the  liquid  tending  to  separate  the  sides  of  the  con- 
taining vessel?  —  Ans.  216g.  The  pressure  of  the  liquid  upon 
the  bottom  is  216g.  But  this  pressure  does  not  tend  to  separate 
the  bottom  if  there  is  no  upward  pressure  against  the  top,  the 


TEST   QUESTIONS.  161 

weight  of  the  liquid  being  supported  by  the  table.  The  pres- 
sure against  each  of  the  four  sides  is  108K,  and  the  force  tend- 
ing to  separate  two  opposite  sides  is  108s;  and  the  entire  force 
tending  to  separate  the  two  pairs  of  opposite  sides  is  therefore 
216*. 

17.  A  man  jumps  from  an  eminence.    During  his  descent  how 
does  the  pressure  of  his  feet  upon  the  soles  of  his  shoes  com- 
pare with  his  weight?     Explain. 

18.  At  what  bight  does  a  water  barometer  stand  when  the 
mercurial  barometer  stands  at  30  inches  ?  —  Ans.    33f  ft. 

19.  In  an  atmosphere  where  the  pressure  is  two  atmospheres, 
how  long  should  a  barometer  tube  be  to  measure  the  atmos- 
pheric pressure  ? 

20.  State  Mariotte's  Law,  and  how  it  may  be  verified. 

21.  In  the  Eight-in-one  apparatus,  why  does  not  water  flow 
from  the  orifices  6,  c,  etc.,  when  the  plug  a  is  out?  —  Ans.   The 
descent  of  the  water  is  unresisted ;  consequently,  there  is  no 
downward  pressure,  and,  for  this  reason,  no  lateral  pressure. 

—  22.  If  a  man  slides  down  a  vertical  rope,  grasping  it  more  or 
less  firmly  with  a  constant  grip,  how  will  the  tension  on  the  rope 
compare  with  his  weight? 

23.  Why/is  there  no  lateral  pressure  in  liquids  falling  freely? 
—  Ans.   There  is  no  pressure  in  such  a  body  of  liquid  in  any 
direction,  inasmuch  as,  according  to  the  supposition,  its  motion, 
caused  by  the  force  of  gravity,  is  unimpeded.      See  Physics, 
p.  44. 

24.  Place  one  body  on  another,  and  allow  them  to  fall  in  a 
vacuum  ;  would  the  former  press  upon  the  latter  during  the  fall  ? 

25.  Show  that  a  body  having  uniform  motion  must  be  in  a 
state  of  equilibrium. 

26.  Why  do  fluids  transmit  pressure  in  every  direction,  while 
solids  transmit  it  usually  only  in  the  direction  in  which  the  force 
acts? 

27.  Why  does  pressure  in  a  body  of  liquid  increase  as  its 
depth,  while  in  a  body  of  gas  it  increases  with  its  depth? 


162  TEST   QUESTIONS. 

28.  Lay  a  piece  of  paper  on  the  smooth  surface  of  a  board, 
and  let  both  drop.    They  reach  the  ground  together  ;  but  if  sepa- 
rated and  dropped  simultaneously,  the  board  reaches  the  ground 
first.     Explain. 

29.  Raise  the  piston  £,  Fig.  43,  p.  60,  to  the  top  of  the  cylin- 
der s,  and  stop  up  the  tube  u  at  its  opening  into  the  cylinder. 
What  force  must  be  applied  to  the  piston  to  pull  it  to  the  bottom 
of  the  cylinder,  the  area  of  the  transverse  section  of  the  piston 
being  20qcm?     Suppose  that  the  piston,  at  the  beginning,  is  at 
the  middle  of  the  cylinder,  will  the  force  required  to  keep  it  in 
motion  be  constant  ?     About  how  great  will  be  the  force  when 
it  reaches  the  bottom  of  the  barrel  ?     Suppose  the  force  at  that 
point  is  withdrawn,  what  will  happen  ?     Suppose  the  apparatus 
to  be  inverted,  and  a  person  were  to  blow  with  a  force  of  10g, 
the  area  of  the  cross  section  of  the  bore  of  the  tube  being  lqcm, 
what  weight  placed  upon  the  piston  might  be  sustained  ?    If  the 
free  extremity  of  the  tube  is  raised  2m  above  the  lower  extremity 
of  the  piston,  and  water  is  poured  into  the  tube  until  it  is  filled, 
what  weight  placed  upon  the  piston  will  be  sustained  by  the 
water?     What  name  would  the  apparatus  receive  in  the  last 
case?    Suppose  that  a  plug,  just  fitting  the  interior  of  the  tube, 
were  forced  into  the  tube  pressing  against  the  water,  what  would 
the  apparatus  become  ? 

30.  The  diameter  of  the  mouth  of  an  air-pump  receiver  is 
20cm.      Three-fourths  of  the  air  has  been  removed  from   the 
receiver.      The   receiver  weighs    1.5k.      What   force   will   be 
required  to  raise  it  from  the  pump-plate? 

31.  A  person  is  on  deck  of  a  vessel  which  is  moving  due  east 
at  the  rate  of  one  mile  an  hour  ;  at  what  rate  must  he  walk  due 
south-west  in  order  that  his  resultant  motion  may  be  due  south  ? 
What  will  be  his  southerly  velocity  ?     (Solve  by  constructing  a 
diagram.) 

32.  A  steamship  is  moving  due  north  at  the  rate  of  10  miles, 
the  tide  carries  it  due  north-east  at  the  rate  of  2  miles  an  hour, 
while  the  wind  carries  it  due  north-west  at  the  rate  of  4  miles  an 
hour  ;  what  is  its  actual  course  and  velocitv  ? 


TEST  QUESTIONS.  163 


33.  A  ship  is  sailing  due  south-west  at  the  rate  of  8  miles  an 
hour  i^hat  is  its  southerly  velocity? 

$£.  A  boat  is  crossing  a  stream  at  the  rate  of  5  miles  an  hour. 
A  person  walks  from  the  stern  toward  the  prow  at  the  rate  of 
3  miles  an  hour.  Describe  his  several  velocities,  and  state  how 
great  they  are. 

35.  While  sitting  in  your  chair,  what  motions  has  the  matter 
composing  your  body  ? 

36.  A  door  stands  ajar ;  why  is  it  not  moved  perceptibly  on 
its  hinges  when  a  bullet  is  fired  through  it? 

o-^Tf.  Draw  an  oblique  line  to  represent  the  path  of  a  boat 
crossing  a  river,  and  find  the  relative  intensities  of  the  current, 
and  the  force  which  propels  the  boat  at  right  angles  with  the 
banks. 

£X#8.  Represent  by  lines  three  forces  acting  at  angles  with  one 
another  on  a  body,  and  find  their  equilibrant. 

39.  In  Fig.  75,  p.  93,  Physics,  what  is  the  relation  of  the 
force  of  gravity  acting  on  the  weight  w  to  the  forces  represented 
by  the  lines  cA  and  cB? 

>^07  Locate  a  point  A  on  your  paper,  and  from  it  draw  a  hori- 
zontal line  AB  to  the  right  to  represent  a  force  of  10  Ibs.,  acting 
on  a  body  at  A.  Draw  from  A  another  horizontal  line  AC  to  the 
left  to  represent  another  force  of  10  Ibs.,  acting  on  the  same 
body  at  the  same  time.  In  what  state  will  the  body  be  as  re- 
gards these  two  forces  ?  What  is  the  relation  of  each  force  to 
the  other  ?  —  Ans.  An  equilibrant.  Show  that  each  force 
produces  its  own  independent  effect  in  accordance  with  the 
second  law  of  motion.  Resolve  one  of  the  forces  into  two 
components.  Let  the  intensities  of  the  two  forces  be  as  8  : 10  ; 
represent  their  resultant,  and  answer  the  requirement. 
£x^  Draw  a  vertical  line  AB.  Let  this  represent  the  path 
in  which  a  body  at  A,  the  lower  extremity  of  the  line,  is  to 
move.  Draw  from  A  a  horizontal  line  AC  to  the  right,  to 
represent  one  force  acting  on  the  bod3\  Construct  a  parallelo- 
gram, and  find  the  direction  and  intensity  of  the  other  force. 


164  TEST  QUESTIONS. 

Letter  the  line  which  represents  it  AD.  "What  is  the  effect  pro- 
duced by  the  force  represented  by  the  line  AC  ?  Show  that 
this  force  produces  the  same  effect  that  it  would  produce  if  the 
force  represented  by  AD  were  not  acting  on  the  body.  In 
order  to  do  this  you  must  suppose  the  force  acting  in  the  line 
AD  to  be  resolved  into  two  components.  What  lines  of  your 
parallelogram  represent  them  ? 

vx^2.  Represent  by  a  parallelogram  a  case  in  which  the  in- 
tensit}7  of  the  resultant  is  less  than  either  of  its  two  compo- 
nents. Explain  why  it  is  less. 

t4#r  (Fig.  75,  Physics.)  Draw  on  the  blackboard  line  CD 
to  represent  the  equilibrant  of  the  force  of  gravity  on  W.  In- 
dicate the  direction  also  of  the  strings  CA  and  CB.  Then,  with 
CD  as  a  diagonal,  and  with  two  of  its  sides  lying  in  the  direc- 
tion CA  and  CB,  construct  a  parallelogram ;  and,  with  the  in- 
tensity of  the  force  represented  ~by  CD  known,  ascertain,  by 
comparing  each  of  the  sides  lying  in  the  line  CA  and  CB  with 
the  line  CD,  the  intensity  of  each  of  the  component  forces. 
Compare  the  results  with  the  readings  of  the  dynamometers  X 
andF. 

The  intensity  of  the  force  CD  and  one  of  its  components  CA 
being  known,  find  the  intensity  of  the  other  component.  Draw 
the  line  CD  of  any  desirable  length.  Draw  a  line  in  the  direc- 
tion CA  as  indicated  by  the  string,  making  its  length  in  com- 
parison with  CD  proportional  to  the  given  forces.  Complete 
the  parallelogram  with  CD  as  a  diagonal,  and  the  line  lying  in 
the  direction  CA  as  one  of  its  sides ;  and  ascertain,  by  com- 
paring the  length  of  the  line  lying  in  the  direction  CB  with  the 
length  of  the  line  CD,  the  intensity  of  the  other  component. 
Verify  the  result  by  consulting  the  reading  of  the  dynamo- 
in^er  T. 

44.  Two  forces  of  20k  and  50k  act  at  an  angle  of  60° ;  find 
their  equilibrant. 

Vx45.  If  two  boats  just  alike  are  connected  by  a  rope,  and  two 
men,  one  in  each  boat,  pull  on  the  rope,  at  what  point  between 


TEST  QUESTIONS.  165 

them  will  they  meet  ?  At  what  point  if  only  one  man  pulls  ? 
Why? 

t^4tT.  State  three  causes  for  the  variation  of  gravity  on  the 
earth's  surface. 

you  move  without  the  aid  of  some  other  body? 
ies  at  rest,  with  respect  to  the  surface  of  the  earth, 
arc  really  in  motion,  and  their  motion  is  not  constant  nor  in  a 
straight  line.    Are  the  forces  which  act  on  them  in  equilibrium? 

/x£tTT  Upon  which  will  the  effect  of  a  given  force  be  greater,  a 
body  at  rest  or  a  bod}'  in  motion  ? 

\J&T  Express  the  atmospheric  pressure  at  sea-level  in  absolute 
units.  —  Ans.  1,012,634  dynes  per  square  centimeter. 

KTl.    Why  are  "top-heavy"  bodies  unstable? 

52.  What  mechanical  advantage  may  be  gained  in  a  copying 
press  in  which  the  hands  move  through  1  inch,  while  the  end  of 
the  screw  descends  y^-  inch?  —  Ans.    F=  142. 

53.  What  is  the  true  wa}-  of  measuring  gravity  or  an}T  other 
force?  —  Ans.    By  its  effects  in  producing  momentum. 

54.  How  many  cubic  feet  of  water  will  a  10-horse-power  en- 
gine raise  in  an  hour  from  a  mine  300  feet  deep,  a  cubic  ft.  of 
water  weighing  62i  Ibs.  ? 

l^o.  When  a  force  acts  on  a  body  at  right  angles  to  the  direc- 
tion of  its  motion,  so  as  to  cause  it  to  revolve  in  a  circle,  does 
it  do  work  on  the  body  ?  Why  ? 

56.  Does  the  sun  do  work  on  the  planets,  which  revolve 
about  it?  Explain.  —  Ans.  No;  the  force  of  its  attraction 
merely  alters  the  direction  of  their  motion,  but  not  their  velo- 
cities, and,  consequently,  not  their  kinetic  energy. 
t/1)7.  What  is  the  weight  of  a  body  at  any  place  ?  —  Ans.  It 
is  its  mass  multiplied  by  the  force  of  gravity  at  that  place 


What  force  is  required  to  lift  one  gram  one  centimeter? 
—  Axis.  980  dynes  in  this  latitude. 

V.X59.    (a)  A  man  whose  weight  is  W  stands  on  the  platform  of 
an  elevator  as  it  descends.     If  the  platform  descends  with  a 


1GG  TEST  QUESTIONS. 

uniform  acceleration  of  :}g,  what  will  be  his  pressure  on  the 
platform?  (6)  What  will  it  be  if  the  platform  ascends  with 
the  same  uniform  acceleration?  —  Ans.  (a)  -J  W.  (b)  J  W. 
\^Q.  A  stone  weighing  15  Ibs.  lying  upon  the  ground  has  a 
spring  balance  attached  to  it.  A  man  raises  the  stone  by 
pulling  the  spring  balance.  Will  the  force  employed,  as  indi- 
cated by  the  spring  balance,  exceed  15  Ibs.,  and  why?  If  it 
exceeds,  upon  what  will  the  excess  depend?  —  Ans.  It  will 
exceed  15  Ibs.,  the  excess  being  employed  in  producing  motion  ; 
and  the  magnitude  of  the  excess  will  depend  upon  the  rapidity 
with  which  it  is  moved. 

V6l.  A  man  carrying  upon  his  shoulders  a  bag  of  sand  weigh- 
ing 100  Ibs.,  jumps  from  an  eminence.  How  great  will  be  the 
pressure  of  the  bag  upon  his  shoulders  during  the  descent,  dis- 
regarding the  resistance  of  the  air?  —  Ans.  There  will  be  no 
pressure,  since  the  man  will  offer  no  resistance,  during  the 
descent,  to  the  action  of  gravity  on  the  sand. 

62.  A  hammer,  whose  weight  is  1500  Ibs.,  falls  10  ft.  How 
far  will  it  drive  a  pile  into  the  earth  against  an  average  resist- 
ance of  10,000  Ibs.  ? 

Go.  What  horse-power  in  a  locomotive  will  be  required  to 
draw  a  train  of  cars  at  the  rate  of  10  miles  an  hour  against  a 
constant  resistance  of  50  tons  ? 

\X)4.  Is  friction  force?  —  Ans.  Yes;  since,  according  to  the 
definition  of  force,  it  tends  to  alter  motion. 

G5.    Is  work  force?  —  Ans.    No  ;  work  is  the  product  of  force 
multiplied  by  the  space  through  which  it  acts. 
i^GG.    What  is   the  product  of  force  multiplied   by  the  time 
during  which  it  acts  called? — Ans.    Momentum. 

67.  When  a  force  acts  upon  a  body  and  causes  it  to  move  a 
given  distance,  in  what  language  would  you  describe  the  effect 
of  the  force?  —  Ans.  As  work  done  on  the  body,  or  as  energy 
communicated  to  the  bod}'. 

G8.  How  does  energy  differ  from  power? — Ans.  The  element 
of  time  has  nothing  to  do  with  energy,  while  power  means  a- 
capacity  to  do  a  given  amount  of  work  in  a  given  time. 


TEST  QUESTIONS.  167 

69.  If  an  engine  should  raise  55  Ibs.  10  ft.  in  a  second,  and 
at  the  end  of  a  second  its  energy  should  be  exhausted,  could 
it  properly  be  called  a  one-horse-power  engine  ?  —  Ans.  Yes  ; 
since  while  it  did  work,  it  performed  at  the  rate  of  33,000  ft.  Ibs. 
per  minute,  and  this  is  just  as  truly  a  horse-power  as  it  would 
be  if  the  work  were  maintained  for  a  thousand  years. 
£/ftf^  A  cannon  ball  is  shot  into  empty  space  ;  how  great  a 
force  will  be  required  to  deflect  it  from  its  path  ?  —  Ans.  Since 
the  body  meets  with  no  resistance,  any  force,  however  small, 
will  suffice  to  deflect  it  from  its  path  in  accordance  with  the 
Second  Law  of  Motion. 

\x?lT  Can  a  child  sitting  on  a  sled  start  or  stop  the  sled  by 
pulling  on  a  cord  attached  to  the  sled?  Why?  —  Ans.  No  ;  since 
the  sled  will,  in  either  case,  receive  both  the  action  and  reaction, 
which,,  being  equal,  would  neutralize  each  other. 

Why  does  not  every  body  move  when  acted  on  by  force  ? 
.   Why  does  a  body  thrown  horizontally  into  the  air  fall  to 
the  earth? 

74.  Is  the  expression  "  one  horse-power  per  second"  admis- 
sible, as,  for  instance,  when  we  wish  to  convey  the  idea  that  a 
horse-power  lasts,  or  is  exerted  for  one  second?  —  Ans.  No  ;  the 
expression  would  be  equivalent  to  33,000  ft.  Ibs.  per  second 
per  second. 

u^To.  How  many  dynes  of  force  are  required  to  set  a  mass  in 
motion  ? 

A^fG.  How  many  dynes  are  required  to  make  a  gram-mass 
move  with  a  velocity  of  9.81m  per  second,  the  force  acting  con- 
stantly for  one  second?  What,  if  it  act  for  two  seconds?  — 
Ans.  981  dynes  ;  490.5  dynes. 

l^fT.  What  is  the  force  acting  on  a  falling  gram-mass  in  the 
Northern  States?  —  Ans.  980  dynes. 

What  is  the  force  acting  on  a  falling  pound-mass  in  the 


Northern  States?  —  Ans.    32.191  poundals. 
l/ffl.    How  many  dynes  are  required  to  set  a  mass  weighing 
50k  in  motion  with  a  velocity  of  12m  per  second,  the  force  acting 
for  precisely  one  second?  —  Ans.   60,000,000. 


168  TEST  QUESTIONS. 

80.  What  kind  of  energy  is  chemical  energy?  —  Ans.  Poten- 
tial energy,  inasmuch  as  it  is  due  to  forces  tending  to  produce  a 
rearrangement  of  molecules.    It  becomes  kinetic  when  chemical 
action,  i.e.  rearrangement,  takes  place. 

81.  What  kind  of  energy  is  the  energy  of  compressed  air?  — 
./4.7is.xKinetic,  since  it  is  due  to  the  motion  of  the  air  particles. 
\^2.    A  body  in  space  is  entirely  free  to  move  (i.e.,  free  from 
the  influence  of  all  other  bodies) ;   how  much  force  will  be  re- 
quired to  move  it?  —  Ans.    A  body  not  constrained  by  other 
bodies  (i.e.,  perfectly  free  to  move)  is  perfectly  sensitive  to  the 
action  of  a  force,  so  that  the  smallest  force  would  move  the 
largest  mass. 

v/83.    Compare  the  velocities  produced  on  masses  of  lk,  200s, 
and  lg  of  forces  measuring  200,000,  40,000,  and  200  dynes.  — 
Ans.   All  equal  if  applied  for  the  same  length  of  time ;  2UOcin 
per  second  if  the  action  endure  one  second. 
V/$4.    Given  a  body  in  motion.     At  a  given  instant  let  it  be 
left  to  itself  and  not  acted  on  by  any  force.    What  will  happen? 
(See  Maxwell's  "  Matter  and  Motion,"  pp.  56,  57.) 

\Jtff.  (a)  Which  has  the  greater  energy,  a  body  moving  at  the 
rate  of  20ra  per  second  in  a  straight  line,  or  one  of  the  same 
mass  moving  with  the  same  velocity  in  a  circular  path?  (b)  If 
the  force  which  compels  the  latter  to  move  in  a  circular  path 
should  cease  to  act,  what  would  be  its  subsequent  velocity  ?  — 
Ans.  (a)  Their  energies  would  be  the  same,  for  energy  does 
not  depend  on  direction  or  form  of  path,  but  on  the  velocit}'  at 
each  instant  along  the  path,  (b)  The  velocity  would  be  20ra 
per  second. 

V^6.  Let  two  equal  forces  act  for  the  same  length  of  time,  one 
on  a  body  weighing  2k,  the  other  on  a  body  weighing  6k ;  how 
will  the  momenta  produced  compare  ? 

87.  Is  a  spring  balance  a  force  measurer  or  an  energy  mea- 
surer ?     Why  will  it  not  answer  both  purposes  ? 

,88.  How  can  a  power  of  5   Ibs.   raise  a  ton   10   ft.  with  a 
perfect  machine? 


TEST  QUESTIONS.  169 

89.  What  power  will  raise  20  tons  of  coal  100  ft.  in  an  hour? 

U>Or~How  many  times  as  much  energy  has  a  body  moving  100 
ft.  per  second  than  another  body  of  the  same  weight  moving 
25  ft.  per  second  ?  Compare  their  momenta. 

^0TT  How  much  faster  will  an  iron  ball  weighing  a  pound  fall 
than  one  weighing  an  ounce  ? 

V^^T  Imagine  that  a  body  having  a  mass  of  40g  is  at  absolute 
rest  in  space,  and  is  absolutely  free  from  the  action  of  all 
external  forces.  Now  let  a  force  of  20  dynes  act  upon  it  for 
five  seconds  in  one  direction.  What  will  be  the  result?  Is 
work  done  upon  the  body  ?  (Inertia  is  not  a  resistance  —  is 
not  a  force.)  When  a  body  offers  no  resistance  to  the  action 
of  a  force,  what  is  the  only  effect  produced  by  the  force  ?  What 
kind  of  motion  is  the  result?  What  kind  of  energy  will  the 
body  acquire,  ?'.e.,  kinetic  or  potential?  What  velocity  will 
the  body  acquire  ?  —  Ans.  2^cm  per  second.  What  amount  of 
energy  will  be  imparted  to  the  body  ?  —  Ans.  50  ergs. 

93.  Is  a  pendulum  which  vibrates  seconds  at  New  York  longer 
or  shorter  than  one  which  vibrates  seconds  at  the  equator? 
Explain. 

94.  Which  will  tick  oftener,  a  clock  having  an  8-inch  pen- 
dulum or  one  having  a  32-inch  pendulum?     How  many  times 
oftener? 

95.  From  the  laws  of  the  pendulum  derive  a  reason  why  a 
person  with  short  legs  naturally  takes  quicker  steps  than  a  per- 
son with  longer  legs. 

96.  Describe   the  transformations  of  energy  that  take  place 
during  a  single  swing  of  a  pendulum. 

97.  Where  will  a  given  pendulum  vibrate  faster,  at  the  top  or 
at  the  foot  of  a  mountain  ?     Why  ? 

98.  Which  will  vibrate    in  a  shorter  time,   a   pendulum   10 
inches  long  or  one  15  inches  long?     How  many  times  shorter? 

99.  Two  clocks  —  one  at  the  equator,  the  other  at  a  pole  — 
have  pendulums  of  the  same  length.     Which  will  gain  on  the 
other,  and  why? 


170  TEST  QUESTIONS. 

100.  It  is  sometimes  necessary  to  use  a  pendulum  less  than  a 
meter  in  length  to  beat  seconds.    How  may  this  be  accomplished  ? 

—  Ans.    By  placing  a  bob  on  the  pendulum  rod  above  as  well 
as  below  the  center  of  motion.     By  moving  this  bob  up  and 
down  the  rod  the  pendulum  may  be  made  to  move  slow  or  fast 
as  is  desirable.     The  musician's  metronome  is  an  example. 
\X01.  A  body  starts  from  rest  under  the  influence  of  a  force 
which  produces   acceleration  a  =  2   feet ;  when  will  it  have  a 
velocity  of  1000  ft.  per  second  ?  —  Ans.    At  the  end  of  the  500th 
second. 

\-^02.  A  body  travels  at  12  ft.  per  second.  In  10  seconds  it 
is  moving  7  ft.  per  second.  What  is  the  mean  retardation? 

—  Ans.  ^  foot  per  second. 

\*^tf)3.  Wherein  is  the  absolute  unit  of  force  preferable  to  the 
gravitation  unit  of  force  ?  —  Ans.  The  former  is  not  affected 
by  the  variations  in  the  force  of  gravity,  and  hence  is  every- 
where the  same,  while  the  latter  is  subject  to  local  variation. 
\.J&i.  The  final  velocity  of  a  falling  body  weighing  5  Ibs.  on 
striking  the  ground  is  100  ft.  per  second.  "With  what  force 
will  it  strike  the  ground  ?  "  —  Ans.  The  question  as  it  stands  is 
devoid  of  sense,  for  the  time  during  which  it  acts  (depending 
upon  the  rigidity  of  both  the  body  and  the  earth)  is  not  given. 
The  question  may  be  stated  thus  :  What  is  the  mean  pressure 
between  the  body  which  has  fallen  and  the  earth  on  which  it 
falls,  if  a  velocity  of  100  ft.  per  second  is  arrested  in  t  units 
of  time  ?  Assume  that  t  is  -^^  of  a  second.  Since  v  =  at  ; 
v  =  100  ;  t=  2A<r  5  a  =  200,000  ;  and  F=  ma  =  ^  x  200,000 
=  31,052.7  + Ibs. 

\xl05.  What  is  the  velocity  of  a  falling  body  at  the  end  of  the 
5th  second  at  a  place  where  g  =  2m  per  second  ?  —  Ans.  10m  per 
second. 

t"i06.  A  bullet  is  fired  from  a  gun  whose  barrel  is  30  inches 
long;  describe  its  motion  through  the  first  30  inches.  —  Ans. 
Its  motion  is  accelerated,  because  it  is  acted  upon  by  a  contin- 
uous (not  constant)  force  throughout  this  distance. 


TEST   QUESTIONS.  171 

When  a  body  is  thrown  horizontally  into  the  air,  why 
does  it  fall  to  the  earth?  What  effect  upon  the  rapidity  and 
time  of  falling  has  its  horizontal  motion? 

108.  Suppose   that  a  cubic  centimeter  of  water  at  4°  C.  to 
become  frozen  :    (a)  What  will  it  weigh?      (6)  What  will  be  its 

nass  ?  Suppose  it  to  be  suspended  by  a  thread  :  (c)  What  ten- 
ion  in  the  thread  will  it  produce,  measured  by  the  gravitation 
jystem?  (d)  What,  measured  by  the  absolute  system?  —  Ans. 
(a)  Weighed  by  a  balance-beam  it  will  weigh  one  gram  ;  weighed 
by  a  spring  balance  it  will  depend  upon  the  locality ;  (6)  its 
mass  is  one  gram;  (c)  the  same  tension  that  would  be  pro- 
duced under  the  same  circumstances  if  a  standard  gram-mass 
(usually  of  platinum)  were  suspended,  and  both  would  depend 
upon  the  locality ;  (d)  measured  by  the  absolute  system  it 
would  depend  upon  the  locality  :  at  sea  level,  in  the  latitude  of 
Greenwich,  it  would  be  981  dynes. 

109.  Suppose  that  you  take  a  cubic  centimeter  of  water  at 
4°  C.  and  allow  it  to  freeze :  (a)  How  will  its  mass  be  affected? 
(6)  What  is  its  density  before  there  is  a  change  of  temperature  ? 
(c)  What,  after  it  is  frozen?     (d)  How  is  its  volume  affected 
by   the    change  ?  —  Ans.    (a)   Its   mass  will  not  be   changed ; 
(&)  its  density  is  1  ;   (c)  its  density  will  be  less  than  1 ;  (d)  its 
volume  will  be  increased. 

110.  In  the  metric   system  what  is  the  density  of  a  body? 
—  Ans.    It  is  the  number  of  grams  in  a  cubic  centimeter. 

111.  Given  a  solid,  a  vessel  of  water  and  a  vessel  of  another 
liquid,  and  a  pair  of  balances  ;  state  how  you  would  find  the 
specific  gravity  of  the  solid,  the  liquid,  and  the  cubical  contents 
of  the  solid. 

112.  State  three  methods  of  finding  the  specific  gravity  of  a 
liquid. 

113.  Suggest  an  easy  method  of  finding  the  cubical  contents 
of   a  test-tube.  —  Ans.    Ascertain  the  weight  of  the  water  it 
contains,  and  the  weight  in  grams  equals  its  contents  in  cubic 
centimeters. 


172  TEST  QUESTIONS. 

114.  A  pebble-stone  weighs  in  air  20K ;  immersed  in  water  it 
weighs  log  ;  immersed  in  another  liquid  it  weighs  17s.     What  is 
the   specific  gravity  of  the  latter  liquid  ?     What  is  the  specific 
gravity  of  the   stone?      What  is  the   cubical  contents  of  the 
stone  ? 

115.  What  is  heat?     Give  some  proof  of  your  statement. 

116.  How  will  you  explain  the  rush  of  air  into  the  vacuum 
when  an  opening  is  made  into  an  exhausted  air-pump  receiver? 

117.  What  is  the  difference  between  a  hot  body  and  a  cold 
body? 

118.  Why  is  the  quantity  of  heat  required  to  raise  the  tem- 
perature of  a  body  of  gas  1°  very  different  when  it  is  in  an  open 
vessel  to  what  it  is  in  a  closed  one  ?  —  Ans.    When  gases  are 
heated  in  an  open  vessel,  they  expand  very  rapidly,  and  a  con- 
siderable portion  of  the  heat  is  expended  in  changing  their  bulk  ; 
in  a  closed  vessel,  the  whole  of  the  heat  is  spent  in  raising  the 
temperature. 

119.  Name  several  processes  by  which  the  temperature  of  a 
body  may  be  lowered  without  removing  heat  from  it?  —  Ans. 
Expansion,  evaporation,  and  liquefaction. 

120.  For  what  purpose  is  ice  wrapped  in  flannels  in  the  sum- 
mer?—  Ans.    To  exclude  the  heat. 

121.  Let  a  kilogram  of  mercury  lose  one  calorie ;  how  much 
will  its  temperature  be  lowered  ? 

122.  How  high  must  a  body  be  raised  that  on  falling  it  will 
generate  enough  heat  to  raise  its  own  weight  of  water  1°  C.  ?  — 
Ans.    Suppose  the  body  weighs  one  pound ;    then  it  must  be 
raised  772  x  f  =  about  1390  ft.      (See  §  147,  Physics.) 

123.  How  many  kilograms  of  ice  at  0°  C.  can  be  melted  by 
lk  of  steam  at  100°  C.  ?  —  Ans.    (537  +  100)  -*-  80  =  7.9k+ . 

124.  How  many  kilograms  of  steam  at  100°  C.  will  melt  100k 
of  ice  at  0°C.?  —  Ans.    (100  x  80)  -r-(537  +  100)  =  12.5k-f. 

125.  What  weight  of  steam  at  100°  C.  would  be  required  to 
raise  500k  of  water  from  0°  C.  to  10°  C.  ? 

Ans.    (500  x  10)  -t-  (537  +  90)  =  7.9k+ . 


TEST   QUESTIONS.  17o 

12G.  A  current  of  9  amperes  worked  on  an  electric  arc-light, 
and,  on  measuring  the  difference  of  potential  between  the  two 
carbons  by  an  electrometer,  it  was  found  to  be  140  volts.  What 
was  the  amount  of  horse-power  absorbed  by  this  lamp  ? 

C1  v  V      0  v  1 4-0 

Ans.  SiA-L  =  J  A  **u  =1.66  horse-powers.    (See rule X.,  p.69.) 
745  745 

127.  How  many  incandescent  lamps,  requiring   an  E.M.F. 
of  CO  volts  and  a  current  of  1.5  amperes  each,  can  be  supplied 
by  an  engine  giving  15  useful  horse-powers,  the  loss  of  energy 
in  the  dynamo  being  20  per  cent? — Ans.    80  per  cent  of  15  =  12, 
the  horse-power  of  current  available.     From  the  tables,  p.  76, 
1   horse -power  =  (about)    746   volt-amperes,    1   lamp   requires 

1.5x60  =  90  volt-amperes:    therefore,  12  *  746  =  1QQ  lampgj 

90 
very  nearly. 

128.  What  amount  of  heat  will  be  generated  in  each  of  the 
foregoing  lamps  per  second  ? 

Ans.    0.00024  X  (1.5  X  60)  =  0.00216  calorie  of  heat. 

129.  An  electric  bell  is  in  circuit  with  a  voltaic  cell  which  will 
furnish  a  current  just  sufficient  to  ring  it.     What  will  be  neces- 
sary if  ten  such  bells  are  introduced  into  the  circuit  ?     Why  ?  — 
Ans.    If  a  given  current  will  ring  one  bell,  it  will  ring  any  num- 
ber of  like  bells.     But  as  each  bell  introduced  into  the  circuit 
increases  the  total  resistance  of  the  circuit,  the  E.M.F.  must 
be  correspondingly  increased  by  the  introduction  of  new  cells  in 
series,  in  order  to  maintain  the  same  current. 

130.  Why  does  it  require  more  voltaic  cells  to  work  a  long 
telegraph  line  than  a  short  one  ?     How  ought  they  to  be  con- 
nected ?     Why  ? 

131.  For  each  50  ohms'  resistance  in  a  circuit,  about  1  gravity- 
cell  is  required  (Haskins) .    Suppose  a  line  of  wire  200  miles  long 
(13  ohms'  resistance  to  the  mile),  and  10  relays  in  the  circuit: 

(a)  What  should  be  the  theoretical  resistance  of  each  relay? 

(b)  How  many  gravit}T-cells  will  be  required  to  operate  them?  — 
Ans.    (a)  Disregarding  the  resistance  of  the  battery  (its  resist- 


174  TEST  QUESTIONS. 

ance  in  this  case  being  relatively  of  no  importance),  the  re- 
sistance of  the  circuit  is  13  x  200  =  2GOO  ohms  ;  hence,  the 
resistance  of  the  relays  should  be  2600  ohms,  or  2GO  ohms  in 
each  relay,  (b)  The  entire  external  resistance  is  2GOO  +  2GOO 
=  5200  ohms  ;  5200  -5-  50  =  104,  the  number  of  cells  required. 

132.  Ten  Bunsen  cells,  whose  E.M.F.  =  1.7  and  r  =  0.5 
ohm,  are  to  be  used  in  a  circuit  whose  JR=2  ohms  :  (a)  What 
will  be  the  current  if  they  are  connected  abreast?  (b)  What,  if 
they  are  connected  tandem?  (c)  What,  if  they  are  joined  in 
pairs  abreast,  and  the  pairs  are  connected  with  one  another 
tandem?  (d)  What,  if  they  are  divided  into  two  groups  of  five 
each,  the  cells  of  each  group  connected  abreast,  and  the  two 
groups  are  connected  tandem? 

Ans.     (a)  C=--j-^  =  Q^+^  =  °'82  amp6rc' 

17    =2.41+  amperes. 


5  +  2 

8.5 

0.25x5  +  2 
3.4 


=  2.G  + 

=  1.72+  amperes. 


0.1  x  2  +  2 

133.  The  resistance  of  5  inches  of  No.  32  platinum  wire  is 
about  0.05  ohm ;  how  would  you  connect  4  Bunsen  cells  so  as 
to  develop  in  the  wire  the  maximum  quantit}"  of  heat? 

Ans.    vW  -f-  E  =  V4  X  0.5  -f-  0.05  =  6+.    The  interpretation 
of  this  is,  that  all  should  be  connected  abreast. 

134.  What  is  the  maximum  amount  of  heat  that  can  be  de- 
veloped in  the  wire  per  second  with  the  four  cells  ? 

-p  IQ 

Ans.   C  = = '- =  10.2+  amperes. 

r  +  E      0.125  +  0.05 

H=C2xExtX  0.00024  =  10.22X  0.05x1x0.00024 

=  0.001248  calorie; 

or,  sufficient  heat  can  be  developed  to  raise  the  temperature  of 
1.248CC  of  water  1°  C.  per  second. 


TEST  QUESTIONS.  175 

135.  What  current  will  there  be  when  10  gravity-cells 
'(E.M.F.  =  1  volt  each,  and  r  =  3  ohms  each)  are  connected  in 
series  through  a  wire  whose  resistance  is  50  ohms  ? 


136.  Show  in  the  preceding  question  that,  with  an  infinite 
number  of  cells  in  series,  the  current  cannot  possibly  exceed 
3^  amperes. 

Ans.   Since  the  external  resistance  in  this  case  will  become 
of  comparatively  no  importance,  it  may  be  disregarded  ;  then 
0  =  g=  IX  infinity  = 
r       ox  infinity 

137.  It  is  required  to  ring  a  bell  over  a  No.  16  copper  wire 
300  ft.  long,  with  three  cells  of  Leclanche"  battery,  the  resist- 
ance of  the  wire  being  0.0076  ohm  per  yard,  and  the  resistance 
of  a  Leclanche"  cell  being  1  ohm.     What  should  be  the"  resist- 
ance of  the  bell  magnet  to  obtain  the  greatest  magnetic  power  ? 
—  Ans.    0.76  ohm  (the  resistance  of  300  ft.  of  wire)  +  3  ohms 
(the  resistance  of  three  cells)  =  3.76  ohms.     The  resistance  of 
the  circuit,  not  including  the  helix   of  the   electro-magnet,  is, 
therefore,  3.76  ohms;  hence  (Law  1  of  electro-magnets),  the 
resistance  of  the  bell  magnet  should  be  3.76  ohms. 

138.  What  is  the  resistance  of  the  carbon  filament  of  an  in- 
candescent light  in  which  there  is  a  fall  of  potential  of  60  volts, 
and  the  intensity  of  the  current  is  1.6  amperes? 

Ans.    JJ  =  ^=^==37iohms. 
C       1.6 

139.  Explain  the  sparks  seen  at  the  circuit-breaker  of  an 
induction  coil  when  in  operation.  —  Ans.    They  are  sparks  pro- 
duced by  the  extra  currents  at  each  "  breaking  "  of  the  circuit. 

140.  A  line  2  miles  long,  built  of  No.   8  iron  wire  whose 
resistance  is  13  ohms  per  mile,  has  two  bell  magnets  in  cir- 
cuit, and  a  battery  of  10  Leclanche"  cells  (r  of  each=  1  ohm). 
What  should  be  the  theoretical  resistance  of  each  bell  masnet? 


176  TEST  QUESTIONS. 

—  Ans.  Battery  resistance  10  ohms  +  line  resistance  2G  ohms 
=  36  ohms.  The  sum  of  the  resistances  of  the  electro-magnets 
should  then  be  36  ohms,  or  18  ohms  each.  But,  as  there  would 
be  likely  to  be  some  leakage,  practically  the  resistance  of  each 
magnet  should  be  some  less  than  18  ohms. 

141.  For  which  is  the  gravity  battery  better  adapted,  circuits 
of   small  or   large  resistance?      Why?  —  Ans.    For  circuits  of 
large  resistance,  since  the  large  resistance  of  the  battery  then 
becomes  of  comparatively  little  importance. 

142.  You  have  48  cells,  each  of  1.2  volt  E.M.F.,  and  each 
of  2  ohms'  internal  resistance.    What  is  the  best  way  of  group- 
ing them  together  when  it  is  desired  to  send  the  strongest  pos- 
sible current  through  a  circuit  whose  resistance  is  12  ohms?  — 
Ans.    Group  them  three  abreast.     (See  Law  VIII.,  p.  69.) 

143.  Required  the  current  in  a  circuit  with  60  Grove  cells, 
connected  in  series  with  12  ohms'  external  resistance;  ?'  =  0.6 
ohm,  and  E  =  1.8  volts  for  each  cell. 

1  n& 

Ans.  C  =  -  =  2.25  amperes. 

36  +  12 

144.  Required  the  current  in  the  same  circuit  when  the  ar- 
rangement of  the  60  cells  is  30  series  of  2  cells  joined  abreast. 

Ans.    C=  — -  —  =  2.56  +  amperes. 

145.  Required  the  current  in  a  circuit,  with  the  same  60  cells 
connected  in  series,  when  R  =  2  ohms.  »• 

Ans.    C  =  —  ^  =  2.85  +  amperes. 

146.  Required  the  current  in  the  last  circuit  with  the  arrange- 
ment of  12  cells  in  series,  each  consisting  of  5  cells  connected 

abreast'  Ans.    C  =  r|^_=  6.27  amperes. 

147.  How  many  Bunsen  cells  (E.M.F.,  1.7  volts  per  cell) 
will  be  required  to  maintain  an  electric  arc-light,  whose  resist- 
ance is  8  ohms,  with  a  current  of  9  amperes? 


TEST  QUESTIONS.  177 

Ans.   0  =  ^-  ;  or,  j£  =  C72=9x8  =  72  volts;  72-4-1.7  =  42+; 
H 

hence,  about  42  cells  will  be  required. 

148.  What  is  the  cause  of  a  current  of  electricity  ?  —  Ans. 
A  difference  of  potential  at  different  points  in  the  conductor 
through  which  it  flows. 

149.  If  two  Bunsen  cells  are  to  be  used  in  a  circuit,  with  an 
external  resistance  of  2  ohms,  should  they  be  connected  abreast 
or  tandem?     If  two  gravity  cells  should  be  used  in  the  same 
circuit,  by  which  method  should  they  be  connected? 

150.  What  E.M.F.  is  required  to  maintain  a  current  of  20 
amperes  in  a  circuit  of  100  ohms'  resistance? 

Ans.    C  =  ^  ;  whence  E  =  C  X  R  =  20  x  100  =  2000  volts. 
H 

151.  What  current  will  a  battery  having  an  E.M.F.  of  4  volts 
furnish  in  a  circuit  whose  total  resistance  is  10  ohms? 

Ans.    (7=-=  — =  0.4  ampere, 
./t       1U 

152.  What  is  the  total  resistance  of  a  circuit  in  which  a  bat- 
tery having  an  E.M.F.   of  2  volts  furnishes  a  current  of  0.5 

ampere?  n      E       ,  „      E        2 

Ans.    C  =  —  ;  whence  R  —  —  =  —  =4  ohms. 

153.  What  is  the  most  convenient  test  of  the  E.M.F.  of  an 
electrical  machine? — Ans.   The  length  of  the  sparks  which  it 
will  give. 

154.  If  a  sounding  body  moves,  how  will  its  motion  affect 
the  wave-length  of  the  waves  which  it  throws  behind?     How 
will  it  affect  those  thrown  in  front  ?     How  will  the  pitch  of  the 
sound  compare  as   heard   by  a  person  in  front  and  another 
behind  ? 

155.  When  a  voice  an  octave  higher,  such  as  that  of  a  woman 
or  boy,  reproduces  the  same  melody  which  has  been  sung  by  a 
man,  we  "  hear  again  a  part  of  what  we  have  heard  before." 
Explain. — Ans.  A  human  voice  conveys  to  the  hearer  not  only 
the  primes  of  the  compound  tones,  but  also  their  upper  octaves, 


178  TEST  QUESTIONS. 

and  with  less  force  the  other  upper  overtones  ;  hence  a  voice  an 
octave  higher  would  produce  the  upper  octave  previously  given 
by  the  man,  or  a  "  part"  of  what  was  previously  given. 

156.  What  kind  of  vibration  is  that  of  a  column  of  air  in  a 
pipe  ?  —  Ans.  Longitudinal. 

157.  The  picture  on  a  stereopticon  slide  is  two  inches  square. 
The  slide  is  ten  inches  from  the  lens  of  a  porte  lumiere.     What 
will  be  the  size  of  the  image  on  the  screen  at  a  distance  of 

30  ft.  ?  —  Ans.  -  =  -,  or  255  =  -  ;    whence  x  =  72  in.  =  6  ft., 

i.e.,  the  image  is  6  ft.  square. 

158.  What  is  the  focal  length  of  the  lens  used  in  the  last 
question  ? 

Ans.  I  +  l=or__  +      =;  whence  /=9.7  +  in. 


159.  At  what  temperature  does  a  body  cease  to  radiate  heat 
and  light?  —  Ans.    It  ceases  to  radiate  heat  at  the  absolute 
zero  ;  light  at  about  525°  C. 

160.  What  phenomenon  shows  that  light  does,  in  a  small 
degree,  pass  around  a  corner?  —  Ans.  Diffraction. 

161.  Why  does  a  white  body  always  appear  of  the  same 
color  as  the  light  by  which  it  is  illuminated  ? 

162.  What  proof  can  you  give  that  the  light  of  the  electric 
spark  does  not  proceed  from  an  incandescent  electric  fluid  (if 
there  be  such  a  substance)'  nor  any  etherial  medium  which  is 
supposed  to  pervade  all  space  ?  —  Ans.  Every  line  found  in  the 
spectrum  of  the  light  proceeding  from  the  electric  spark  can  be 
traced  to  some  chemical  substance  existing  either  in  the  elec- 
trodes or  in  the  space  through  which  the  electricity  passes,  and 
there  are  none  that  are  common  to  all  discharges,  as  would  be 
the  case  if  a  common  medium  were  rendered  luminous. 

163.  A  gas-burner  must  have  what  candle-power  in  order  that 
it  may  illuminate  a  printed  page  as  brightly  at  a  distance  of  5  ft. 
as  a  single  candle  at  a  distance  of  1  ft.?  —  Ans.  25  candle- 
power. 


TEST  QUESTIONS.  179 

164.  How  does  one  color  differ  from  another  color? 

165.  How  do  you  explain  the  separation  of  colors  when  white 
light  passes  through  an  optical  prism  ? 

166.  What  is  the  general  effect  of  a  concave  mirror  on  a 
beam  of  light?     Name  some  other  piece  of  optical  apparatus 
that  will  produce  the  same  effect. 

167.  Why  is  the  image  of  a  light  as   seen  in  water  usually 
enormously  elongated  vertically  ? 

168.  Why  is  the  same  side  of  the  moon  always  turned  toward 
the  earth  ?     Does  the  moon  rotate  on  its  axis  ? 


PAET  V. 

SOLUTIONS  TO  PROBLEMS   IN  ELEMENTS 
OF   PHYSICS. 


CHAPTER    II. 
DYNAMICS. 

PAGE  52.    Q.  4.     76  :  49.2  ::  1033.3  :  668. 92*+. 

Q.  5.     76:  98. 2::  1033.3:  1335.13*  +  . 
PAGE  60.    Q.  8.     Any  weight  less  than  10k  may  be  lifted. 

PAGE  68.  Q.  3.  The  pressure  on  the  top  is  nothing;  on 
the  bottom  it  is  25  x  20xl5g=  7500g;  on  each  of  the  sides  it 
is  25  x  15  x  7.5*=  2812.5*;  and  on  the  ends,  20  x  15  X  7.5* 
=  2250*. 

Q.  4.  The  additional  pressure  will  be  100*  for  every  4qcm  of 
area  on  the  inner  surface.  The  area  of  the  bottom  is  500qcm ; 
the  additional  pressure  is,  therefore, 

^X  100*  =  12,500*. 
4 

This,  also,  is  evidently  the  pressure  on  the  top.    The  additional 
pressure  on  each  of  the  sides  is 
375 


X  100*  =  9375*; 


and  on  each  of  the  ends, 


—  X  100*  =  7500*. 
4 


182  SOLUTIONS  TO  PROBLEMS. 

PAGE  G9.  Q.  5.  The  total  pressure  on  the  bottom  is  7500g 
+  12,500*=  20, 000";  that  on  the  top,  12,500*;  on  each  side, 
12,187.5g;  on  each  end,  9.750*. 

Q.  G.  The  answers  to  Q.  3  would  be  13.G  times  greater: 
viz.,  102,000*  on  the  bottom  ;  38,250*  on  each  side,  and  30, GOO* 
on  each  end. 

In  considering  Q.  4,  it  makes  no  difference  whether  mercury 
or  water  is  used.  In  the  case  of  mercury,  the  total  pressure  on 
the  bottom  is  evidently  102,000*  + 12.500*=  114,500- ;  on  the 
top.  12,500*;  on  each  side,  38, 250*  +  9375*  =  47, G25* ;  and  on 
each  end,  30,600*  +  7500''  =  38,100*. 

Q.  7.  (a)  The  pressure  on  the  bottom  of  the  keg,  when  the 
tube  is  empty,  is  evidently  1200*.  (6)  If  the  tube  be  filled, 
the  column  of  water  will  be  1030cm  high,  instead  of  30cm  ;  there- 
fore the  pressure  on  the  bottom  is  40  X  1030  =  41 ,200*.  (c)  The 
weight  of  the  water  in  the  tube  is  evidently  1000*. 

Q.  8.  Assuming,  for  simplicity,  that  all  parts  of  the  box  are 
at  equal  depths,  the  crushing  force  on  each  side  would  be  equal 
to  the  weight  of  a  column  of  water  lkra  high,  with  a  base  of  lqm  ; 
the  volume  of  this  is  1000cbm,  and  its  weight  l,000,000k. 

Q.  9.  Taking  the  atmospheric  pressure  at  lk  per  square 
centimeter,  the  crushing  force  at  the  sea  level,  on  each  sido, 
would  be  10,000k. 

Q.  10.  Since  the  whole  area  of  the  top  is  500qcra,  a  pressure 
of  20*  on  the  plug  would  make  a  total  pressure  of 

—  X  20*  =  2500*  : 

but,  by  the  conditions  of  the  problem,  the  top  can  sustain  50* 
on  each  10qcrn,  or  2500*  total;  therefore,  it  is  clear  that  any 
pressure  on  the  plug  greater  than  20*  would  burst  the  vessel. 

PAGE84.    Q.I.     1033. 3  -*- 1.841  =  561. 27cm-f. 
Q.  2.     The  50*  of  water  when  immersed  in  water  is  evidently 
buoyed  up  with  a  force  of  50*,  and  no  weight  is  indicated. 


CHAPTER   II.  —  DYNAMICS.  183 

Q.  n.    The  combined   solids  displace   102.  88°°.      The  sinker 
alone  displaces  14CC  ;   102.88CC-  14CC  =  88.88CC  ;  hence, 


Q.  4.  The  weight  of  the  water  displaced,  or  the  buoyant 
force  when  the  oil  is  completely  immersed,  is  greater  than  the 
weight  of  the  oil  ;  we  have,  then,  two  unequal  forces  in  opposite 
directions,  and  the  oil  rises  until  the  weight  of  the  water  dis- 
placed just  equals  the  weight  of  the  oil. 

Q.  5.  In  the  case  of  a  floating  tumbler,  it  will  be  noticed 
that  by  far  the  larger  part  of  the  water  displaced  is  displaced 
not  by  the  glass  simply,  but  by  the  air  in  the  bottom  of  the 
tumbler,  and  the  average  density  of  the  combination  of  air  and 
glass  is  less  than  the  density  of  water,  so  the  tumbler  floats. 

Q.  G.  Iron  vessels  float  for  the  same  reason  that  the  tumbler 
does. 

Q.  7.  From  the  table  of  specific  gravities,  we  find  that  I**5  of 
ioe  weighs  0.92g,  then  500CC  weigh  4GOg  ;  460g  or  460CC  of  water 
will  be  displaced,  so  that  500™  —  460CC,  or  40CC,  of  ice  will  be 
t,bove  the  surface. 

Q.  8.  Ice  will  sink  in  alcohol,  since  its  specific  gravity  is 
greater  than  that  of  alcohol. 

Q.  9.  The  weight  of  500CC  of  fresh  water  is  500g,  that  of 
oOO**  of  sea  water  is  500  x  1.026*  =  513g,  making  13g  more 
matter  in  the  sea  water  than  in  the  fresh  water. 

Q.  10.     ^5M=2582.64CC+. 
19.36 

Q.  11.     19.36s  per  cubic  centimeter. 
Q.  12.     0.24g  per  cubic  centimeter. 
Q.  13.     ^g  (0.0012932g)  per  cubic  centimeter. 
Q.  14.     The  53g  lost  weight  is  the  weight  of  an  equal  bulk  of 
water,  so  the  volume  of  the  marble  is  53CC. 


184  SOLUTIONS   TO   PROBLEMS. 

Q'16'     0^012932  =  778'27CC+- 

PAGE  85.    Q.  17.     G  =21,  or  8.79  =  i°°?  ; 
W  W 

•••W=^?=  113.768  =  weight   of   an   equal  bulk  of   water. 
o.  /y 

The  piece  of  copper,  therefore,  weighs  in  water  1000g—  113.  76g 

=  886.242. 

Q.  18.     The  cubical  contents  is  20  x  10  x  5cm  =  1000CC  ;  there- 
fore the  weight  is  1000  x  11.35  =  11,350*. 

Q.  19.     It  will  lose  the  weight  of  an  equal  bulk  of  water, 
viz.,  1000g;  thus  weighing,  when  immersed,  10,350*. 

Q.  20.     Lead  will  float  on  the  surface  of  mercury. 

Q.  21.     The  weight  that  is  lost  is  transferred  to  the  liquid. 
(See  Exp.  2,  p.  76.) 


Q.».  -  1.015. 


Q.  23.     F==  =  88.10cc+  ;  the  weight  of  an  equal 


volume  of  air  is  88.1  x  0.0012932*  =  0.11393092g+  =  the  weight 
gained  by  weighing  in  a  vacuum  ;  therefore,  the  weight  in  a 
vacuum  is  1  000.  11  39309  2g-f  . 

Q.  24.     The  specific  gravity  of  the  other  liquid  is 

30  ~27 


30-26      4 


=    =  0.75. 


Q.  25.     (?  =      ,orTr'  =     =i         =  14.3^+  =  the  weight 

supported  by  the  water  ;  150B—  14.32g  =  135.68g+,  the  weight 
supported  by  the  string. 

Q.  26.     The  weight  of  the  boat  is  evidently  the  weight  of 
25cbm  of  water,  or  25,000k. 

Q.  27.     It  would  displace  50k  of  water  more,  viz.,  25,050k. 


CHAPTER   II.  —  DYNAMICS.  185 

Q.  28.  100cbm  of  water  weighs  100,000k  ;  the  boat  alone 
weighs  25,000k  ;  therefore,  it  will  take  75,000k  to  sink  the  rail 
to  the  water-level. 

Q   29       105.928  -100  =  5.928  =  217 
102.4    -100        2.4 

Q.  30.  I1  of  water  weighs  1000g  ;  the  density  of  alcohol  is 
0.8  ;  therefore,  I1  of  alcohol  weighs  800g. 


Q.  32.     F=-  =  —  =  56.33CC+. 

Q.  33.    TF=Fx  Z>  =  35x0.847  =  29.  645*. 

Q.  34.  Each  square  centimeter  must  be  able  to  sustain  the 
weight  of  a  column  of  water  2000cm  high,  or  2000g  =  2k  per 
square  centimeter. 

Q.  35.  The  bottom  sustains  2500  x  50  =  125,000*=  125k  ; 
each  side  sustains  one-half  of  this,  viz.,  62.  5k. 

Q.  36.  It  will  sink  a  little  way,  for  the  buoyant  effect  of  the 
air  on  the  part  not  immersed  in  the  liquid  will  be  removed. 

PAGE  96.  Q.  1.  Let  a;  represent  the  distance  from  the  boy 
that  the  weight  should  be  placed, 

a:  3  -a::  30:  20;  whence,  x  =  1.8m. 

Q.  2.  40  :  260  ::  50  —  x  :  x  ;  or,  x  =  43.33k+  =  weight  sup- 
ported by  the  man  ;  so  the  boy's  load  is  6.66k  +  . 

Q.  3.     Half  a  mile  down  the  stream. 

Q.  4.     £  V2  miles. 

Q.  5.     Half  an  hour. 

Q.  6.     %  V2  x  10  =  5  V2  miles  per  hour. 

PAGE  107.    Q.I.     S  =  ^T2  =  £x  9.8rax  25=122.5™ 

=  £  X  321  ft.  x  25  =  402.08  +  ft. 
Q.  2.      s  =  ^(2Z7-l)  =  £x9.8mx9  =  44.1m 

=  J  X  32J-  ft.  x  9  =  144.74  +  ft. 


186  SOLUTIONS   TO   PROBLEMS. 

Q.  3.     F=#r=9.8m  X  5  =  49.0m  =  32J  ft.  X5=160.83+ft. 

Q.  4.     £  =  %gT*  =  J  X  9.8™  X  49  =  240.1"  =  £  X  32  J-  ft.  X  49 
=  788.08  +  ft. 

Q.  5.     S  =  $kT*  =  500™  X  3GCO  =  1  ,800,000m 

=  1640.42  ft.*  X  3600  =  5,905,512  +  ft. 

Q.  6.     F=  £fc  X  2T  =  500mx  60  =  30,000m  per  minute 

=  1640.42  ft.  x  60  =  98,425.2  ft.  per  minute. 

Q.  7.      s  =  p(2!F-l)=500m  X  117  =  58,500™ 

=  1640.42  ft.  X  117=  191,  929.  14  +  ft. 

Q.  8.     S  =  PT2  =  2m  X  16  =  32In  =  6.56+ft.  X  16  =104.96  ft. 
from  a  point  directly  under  that  from  which  it  started. 

Q.  9.     F=px277=2mx8  =  16m  =  6.56  ft.  X  8  =  52.48  ft. 

per  second. 
Q.  10.  F=  gT  =  9.8m  x  4  =  39.  2m  =  32£  x  4  =  128.66  +  ft. 

per  second. 
Q.  11.  V=gT=  9.8m  x  3  =  29.4m  =  321  x  3  =  96.5  ft.   pel- 

second. 

Q.  12.  It  will  rise  in  the  first  second  as  far  as  it  would  fall  in 
the  third. 


=  80.41  +  ft. 

PAGE  111.  Q.  1.  They  would  vibrate  in  equal  time,  since 
the  accelerative  effect  of  gravity  on  all  bodies  is  the  same  at  the 
same  place, 

Q.  2.     1  :  4  ::  V0.993  :  V5,  or  #  =  0.248m 

=  the  length  of  a  pendulum  beating  half  -seconds. 

1  :  i  ::  VOT993  :  VoJ,  or  x  =  0.062M 

=  length  of  one  beating  quarter-seconds. 

1:2::  V0.993  :  VoJ,  or  x  =  3.972m 

=  length  of  one  beating  once  in  two  seconds. 

0.3048m. 


CITAr-TEE    II.  —  DYNAMICS.  187 

1  :  30  ::  V0.993  :  V»,  or  05  =  893.7™ 

=  length  of  one  beating  once  in  thirty  seconds  or 
twice  each  minute. 

p  f\ 

Q.  3.     1 :  —  ::  Vo.yytf  :  Vo74  where  both   lengths  are  ex- 

M£ 

pressed  in  meters,  and  a?  is  the  required  number. 

PAGE  116.  Q.  1.  Momentum  =  mass  x  velocity  s=  100,000 
X  J-  =  16,666.66 -f  for  the  car,  where  the  mass  is  expressed  in 
pounds  and  the  velocity  in  feet  per  second.  The  momentum  ot 
the  ice  =  500  x  96.5  =  48,250 ;  so  the  momentum  of  the  ice  is 
nearly  three  times  that  of  the  car. 

Q.  3.     25  x  =  80  X  1 0  =800  ;  therefore  x  =  32kttl  per  hour. 

Q.  4.  To  double  the  momentum  with  a  constant  mass,  the 
velocity  must  be  doubled  ;  to  double  the  velocity  the  time  must 
be  doubled ;  but,  by  doubling  the  time  a  body  is  falling,  the 
space  is  increased  four-fold. 

PAGE  130.   Q.  5.    The  work =80x4x60  =  19, 200k*m  per  hour. 

Q.  6.  (a)  Falling  freely  for  4  seconds,  a  body  would  fall 
through  a  space  S  =  %gT*,  or  4.9  x  16  =  78. 4m  ;  therefore,  in 
order  that  a  body  weighing  50s  may  rise  78. 4m,  energy  equal  to 
0.05  X  78.4,  or  3.92kgm,  must  be  imparted  to  it. 

(b)  Here  S  =  4.9  X  25  =122.5m,  and  the  energy  will  be  0.05 
X122.5  or  6.125kgm  =  ff  of  3.92kgm ;  i.e.,  the  energy  required 
to  cause  a  body  to  rise  5  seconds  is  ff  of  that  required  to  cause 
it  to  rise  4  seconds. 

(c)  The  reason  of  this  is  that  the  initial  velocity  necessary  to 
enable  a  body  to  rise  5  seconds  is  J  of  that  which  would  enable 
it  to  rise  4  seconds,  and  the  energy  increases  as  the  square  of 
the  velocity. 

Q.  7.  Since  the  momentum  of  any  moving  body  is  propor- 
tional to  the  velocity  ;  and  since,  in  falling  bodies,  the  velocity 
varies  as  the  time,  it  follows  that  the  momentum  in  the  case  (b) 
above  is  f  of  that  in  (a) . 


188  SOLUTIONS  TO  PROBLEMS. 

Q.  8.     Since  the  energy  =  weight  into  hight  (Ws)  ,  the  energy 
stored  in  50k  80m  high  is  50x80  =  4000kgm. 


Q.9.     Energy  =          =  =  25,510.20^+. 


Q.  10.     S  =  %gT2  =  4.9  X  16  =  78.4m  ; 

energy  ==  WS  =  50  x  78.4  =  3920kgm. 

Q.  11.     If  the  50k  should  fall  in  air,  a  part  of  its  energy 
would  be  transformed  into  heat. 


Q.  12. 

Q.  13.  During  the  ascent  its  energy  is  expended  in  doing 
work  by  lifting  the  25k  to  a  hight  against  the  force  of  gravity. 

Q.  14.  (a)  Momentum  =  M V—  50  X  2  =  100  ;  again,  for  the 
50g,  with  a  velocity  of  100m  per  second,  we  have  :  momen- 
tum =  M F=0.05  x  100  =  5  ;  therefore  50k  moving  2m  per  second 
has  20  times  the  momentum  of  50g  moving  100m  per  second. 

(6)   Energy  = 


2x9.8 


MV2     0.05  x  9,  -lkgm 

again,  energy  =  —  =      -y^^ 

i.e.,  the  energy  in  the  second  case  is  |-  of  that  in  the  first. 

Q.  15.  Energy  is  the  power  of  doing  work  ;  work  is  the 
overcoming  of  resistance  through  space  ;  therefore  it  is  its 
energy  that  enables  one  to  determine  the  amount  of  resistance 
that  a  moving  body  can  overcome. 

Q.  16.  A  child  can  draw  a  carriage  weighing  150k  because 
the  energy  required  to  overcome  the  resistance  offered  by  the 
revolving  wheels  is  much  less  than  that  required  to  raise  30k 
against  the  force  of  gravity. 

Q.  17.  (a)  The  work  of  the  horse  is  equivalent  to  that  of 
raising  40k  100m  per  minute  =  4000kgm  per  minute. 

(6)   Since   1  horse-power  =  45  70kgm  per  minute,  4000kgm  per 


minute  =  h.p.  =0.87  +h.p. 

45/0 


CHAPTER    IF.  —  DYNAMICS.  189 

Q.  18.     3km  per  hour  =  50m  per  minute;  the  power  required 

to  move  70k  50m  per  minute  is  3500kgm  per  minute  =  35QQ  b.p. 

4570 
=  0.7G-f-h.p. 

Q.  19.     5ra  per  hour  =  -^m  per  minute  ;  to  raise  1,350,  000k  y1/1 
will  require  T^  of  l,350,000kgra  of  work  per  minute  =  112,500kgm 


Q.  20.  10  tons  =20,000  Ibs.;  a  3  h.p.  engine  will  raise 
99,000  Ibs.  1  ft.  in  1  minute,  or  ^  of  99,000  =  1980  Ibs.  50  ft. 
in  1  minute  ;  therefore,  to  raise  20,000  Ibs.  50  ft.,  it  will  take 


Q.  21.  A  2  h.p.  engine  will  raise  2x4570k  =  9140k  lm  per 
minute;  in  10  seconds  the  same  engine  will  raise  ix9140k 
=  1523ik  lm  ;  therefore,  in  the  same  time  it  wiU  raise  1000k 
15231 


=  1.523™  +  - 
1000 

Q.  22.     A  5  h.p.  engine  can  do  5x4570kgm  of  work  per  min- 
ute, or  60  x  5  X  4570kgm=  l,371,000kgm  per  hour. 


Q.  24.  The  energy  increases  as  the  square  of  the  velocity  ; 
therefore,  to  increase  the  energy  four-fold,  the  velocity  must 
be  doubled. 

PAGE  135.  Q.  1.  (a)  Since  the  power,  multiplied  by  the 
distance  through  which  it  moves,  must  equal  the  weight  multi- 
plied by  its  distance,  it  is  clear  that  the  10k  will  be  moved  with 
a  velocity  of  2m  per  second. 

(b)  -f-g-  =  0.4m  per  second. 

Q.  2.  Pp  =  Ww',  .-.  50xlOO  =  2TF,  or  TF=2500k.  The 
advantage  would  be  one  of  convenience,  since  a  small  power 
moving  through  a  considerable  distance  can  move  a  very  great 
weight  through  a  short  distance.  In  common  parlance  we  should 
say  that  "power"  is  gained. 


190  SOLUTIONS  TO  PROBLEMS. 

-.    „       W      p          4  p 

Q.  G.      — =  ±- ,  or  -=s  --  ;  .-.p=50cm,  i.e.,  the  prop  must 

P      w         2      7.5—7? 

be  50cm  from  the  power  end.  The  pressure  on  the  prop  will  be, 
clearly,  2  +  4  =  6k  added  to  the  weight  of  the  lever. 

Q.  9.  Suppose  the  prop  to  be  afin  from  the  end  from  which 
5k  are  suspended,  then  5x  =  20  (70  —  x) ,  or  x  =  5Gcm. 

Q.  11.     3TF=15xl,  or  TF=51bs. 

PAGE  136.  Q.  12.  6  x  3  =  1  x  #,  or  the  number  of  spaces  of 
P  from  the  fulcrum  is  18. 

Q.  13.  The  power  multiplied  by  its  distance  must  equal  the 
weight  multiplied  by  its  distance,  i.e.,  240P=  GO  x  40,  or  P=  10. 

Q.  14.  I0m=1000cm;  since  the  circumference  of  the  axle 
=  60cm,  it  will  take  ^4^=  16|  turns  to  raise  the  bucket  from 
the  cavity.  The  power  at  each  turn  travels  240cra ;  therefore, 
the  whole  distance  that  the  power  must  travel  is  16fx240cm 
=  4000cm=40m. 

Q.!5.     (.)£_£,     orJF=f;,.TF=91b, 

w1     ^n 

(6)  Again,  ^-«~5  •'.  ^=451bs. 
y        o 

TITff         AC) 

(c)  Again,  ^-  =  —  ;  .-.  TT"=  225  Ibs. 

45        8 

(d)  W"  X  its  velocity  =  P  X  its  velocity;  .  • .  P's  velocity  would 
be  225x5  ft.  =  1125  ft.  per  second. 

Q.  16.     The  action  of  the  wheel  and  axle  is  the  same  as  that 
of  a  lever  of  which  the  fulcrum  is  at  the  centre  of  the  axle  ; 
P__  radius  of  axle 
W     radius  of  wheel 

if  the  axle  is  a  pinion,  and  the  wheel  has  teeth  by  which  it  is 
turned  by  another  wheel,  then,  since  the  circumferences  are  to 

P  N* 
each  other  as  their  radii,  — -  =  — ,  where  N=  the  number  of 

W  N 
teeth  on  the  wheel,  and  N'  —  the  number  on  the  axle. 


CHAPTER   III.  —  HEAT.  191 

Q.  17.     Applying  the  same  principle  that  we  have  used  so 

W     p 
often,  we  have—  =— ,  where  p  and  w  mean  vertical  distances. 

In  the  case  of  the  inclined  plane,  p  =  L  and  w  =  H\  therefore, 

TTA  T 

the  general  formula  becomes  —  =  —  . 

Q.18.     lT=£;,.^4'<^=5°lb8- 

Q.  19.  As  in  the  case  of  all  simple  machines,  so  in  the  screw 
Pp  =  Ww,  i.e.*  25xl47r  =  ^TF;  whence,  IF,  or  the  pressure 
beneath  the  screw,  is  4398.24  Ibs.  We  have  supposed  here 
that  the  parts  move  without  friction. 

PAGE  137.  Q.  20.  Here  P  moves  through  10cm,  and  W 
through  100  —  98  =  2cm ;  therefore,  a  force  of  80g  applied  in 
the  direction  cd  will  exert  a  lateral  pressure  of  ^  X  80g  =  400g. 


CHAPTER   III. 

HEAT.  » 

PAGE  148.  Q.  4.  The  cubical  contents  of  the  room  is  3x3 
X2.5m=22.ochm=22,500cdm;  since  each  person  breathes  9cdm 

of  air  per  minute,  two  persons  will  be  supplied  — —  minutes 

=  1250  minutes  =  20f  hours. 

Q.  5.  For  1000  persons  1000"bm  of  fresh  air  is  needed  to 
keep  the  whole  mass  from  becoming  vitiated  ;  the  room  contains 
(35  X  18  x  7cbm)  =  4410cbm  ;  therefore  a  complete  change  once  in 
4.41  minutes  is  necessary. 

PAGE  153.  Q.  1.  Since  1°  C.  =  f  of  1°  F.,  80°  C.  =  -f  of 
80°  F.  =  144°  F. 

Q.  2.     Since  l°F.  =  f  of  1°C.,  30°  F.  =  |  of  30°  C.  =  16|°  C. 


192  SOLUTIONS   TO   PROBLEMS. 

Q.  3.      (a)   The  temperature  of  the  room,  after  the  fall,  was 
clearly  68°- 30°=  38°  F. 

(b)    C.=f  (F.-32)  =  f  (68°-32°)=200  C.  before  the  fall; 
and  f  (38° -32°)  =  3^°  C.  after. 
PAGE  154.    Q.  4.     |C.  +  32  =  F.  ; 

.-..  100°C.=  212°F.  -20°C.  =  -    4°F. 

40°       =104°  -40°       =-40° 

56°       =132f°  80°      =    170° 

60°      =140°  150°       =    302° 

0°       =    32° 
Q.  5.     f(F.-32)  =  C.; 

.-.  212°  F.=    100°  C.  -10°  F.  =  -23i°  C. 

32°       =        0°  -20°       =  — 28f° 

90°       =      32|°  -40°       =-40° 

77°       =      25°  40°       =        4f-° 

2Q°       =_    6|°  59°       =      15° 

10°       =-12|°  329°       =    165° 

PAGE  156.  Q.  1.      Absolute   temperature  equals 

C.+  273°=F.  +  460°; 
therefore,  mercury  boils  at 

(350°+ 273°)  C.=  623°C., 
or  (662°+ 460°)  F.=  1122°  F. 

Mercury  freezes  at  (- 38.8°+ 273°)  C.=  234.2°  C., 
or  (-37.8°+ 460°)  F.=  422.2°  F.=  abs.  temp. 

Q.  2.     (a)  The  increase  in  volume  will  be 

•ffo  of  500  =  137.36CC+  ; 

therefore,  the  total  volume  at  75°  C.=  637.36CC+. 
(b)  In  this  case  the  decrease  will  be 
••ffcof  500CC  =  36.63CC+, 
so  that  the  final  volume  will  be 

(500  -  36.63cc-h)  =  4G3.37CC+. 

PAGE  157.    Q.  4.     30°  C.=  303°   absolute   temperature,   and 
-15°  C.=  258°  absolute  temperature  ;   I1  =  1000CC ; 
.-.  303  :  258  ::  1000  :  351.48CC  +  . 


CHAPTER   III.  —  HEAT. 


193 


Q.  5.  Calling  the  pressure  of  one  atmosphere  1000g  per 
square  centimeter,  we  have  the  proportion 

900:  1000::  1000:  11  ll^*. 

Q.  7.  1000  x  1 :  1  X  200  ::  273  :  54.6°  absolute  temperature, 
or  -  218.4°  C. 

Q.  8.  Melting  Points. 

Alcohol Always  liquid 

Mercury  234.2°  C. 

Sulphuric  acid 238.6° 

Ice 273° 

Phosphorus 317° 

Sulphur 388° 

Tin about     506° 

Lead 607° 

Zinc 698° 

Silver 1273° 

Gold 1473° 

Cast-iron 1323-1523° 

Wrought-iron 1773-1873° 

Iridiura 2223° 

Q.  9.  When  the  barometer  is  at  30  in.,  the  pressure  is 
15  Ibs.  per  square  inch;  and  when  it  is  at  29  in*.,  the  pressure 
is  f-g-  of  15  lbs.=  14.5  Ibs.  per  square  inch. 

32°  F.  =  492°  F.  absolute  temperature  ;  68°  F.  =  528°  F.  abso- 
lute temperature ;  hence,  we  may  write  the  compound  propor- 
tion 


Boiling  Points. 

Carbonic  acid 195°  C. 

Ammonia 233° 

Sulphurous  acid 263° 

Ether 308° 

Carbon  bisulphide 321° 

Alcohol 351° 

Water 373° 

Mercury 623° 


528  :  492 
15 :  14.5 


1 


25    27.7 

PAGE  173.  Q.  1.  To  convert  lk  of  ice  at  0°  C.  into  water 
at  0°  C.  requires  80  calories;  to  raise  it  to  the  boiling  point 
requires  100  calories  more,  and  to  change  this  water  into  steam, 
537  calories  are  necessary.  The  total  heat  that  disappears  in 
the  change  is,  therefore,  80  +100  +  537  =  717  calories  for  each 
kilo,  i.e.,  71,700  calories  for  100k. 

Q.  2.  (a)  In  condensing  1000k  of  steam  at  100°  C.  into 
liquid  at  100°  C.,  1000x537  =  537,000  calories  are  liberated ; 


194  SOLUTIONS   TO   PROBLEMS. 

in  falling  from  100°  C.  to  80°  C.,  the  heat  given  off  is  evidently 
1000x20  =  20,000  calories,  making  a  total  of  557,000  calories 
given  out  to  the  building. 

(6)  lk  of  water  requires  100  calories  to  raise  it  from  0°  C.  to 
100°  C.  ;  with  557,000  calories,  then,  we  can  raise  5570k  to  the 
same  temperature. 

Q.  3.  50k  of  water  at  100°  C.  can  impart  5000  calories  to  the 
ice  ;  to  melt  lk  of  ice  at  0°  C.  takes  80  calories  ;  the  amount  of 
ice  that  may  be  melted  is,  then,  ^f|^k  =  G2.5k  =  137.73  +  Ibs. 

Q.  4.     0.504  x  10  +  80  +  10  =  95.04  calories. 

Q.  5.  (a)  When  the  water  is  at  the  boiling  point,  100°  C., 
100  calories  have  been  used  for  each  kilo ;  the  ice  has  been 
converted  into  water  at  20°  C.,  (b)  each  kilo  having  consumed 
80  calories  in  melting. 

Q.  7.  If  we  call  the  resulting  temperature  T°,  following  the 
experiment  with  the  sheet  lead,  we  have  the  equation  :  — 

T 

=  specific  heat  of  iron  =0.1138  ; 

100  —  J. 

or  1.11387=11.88;  whence  T=  10.21°+  C. 

Q.  8.     ^r.  =  specific  heat=  0.052C  +  . 

Q.  9.  50k  of  water  at  80°  could  transmit  4000  calories  ;  but 
the  specific  heat  of  mercury  is  0.0333  ;  therefore  50k  of  mercury 
at  80°  can  transmit  only  0.0333  of  4000  =  133.2  calories.  Hence 
133.2 -r- 80  =l.GG5k. 


CHAPTER   IV. 

ELECTRICITY   AND    MAGNETISM. 
PAGE  204.    Q.  1.     From  the  table  (p.  203)  we  see  that  the 

f*     4f* 

ratio  of   the   relative  resistances   of   iron   and  copper  is  — — 

1.06 

=  6.09+  ;   •'•  G.09  -f  miles  of  copper  wire  offers  the  same  resist- 
ance us  one  mile  of  iron  wire  of  the  same  size. 


CHAPTER  IV.  —  ELECTRICITY  AND  MAGNETISM.        195 

Q.  3.  By  referring  again  to  the  table,  it  is  seen  that  by  the 
addition  of  the  acid  the  conductivity  is  made  about  5000  times 
greater. 

n    A       2000000  P  ~m  ,-  ,    +• 

Q.  4.     —    —  =  1  ,886,  792.  45  -f  times. 
1.06 

Q.  5.  Employ  plates  of  large  surface,  and  place  them  near 
together. 

Q.  6.     R  =  9.  72x^|  =  24.7+  ohms. 
Q.  7.      l  =  9.72x|;  .-./  =  3.7+ft. 

Q.  8.    72=  127.3  x—  =  31.1  +  ohms. 
142 


Q.  9.     72=59.1  x          =  10.1  +  ohms. 
1752 

PAGE  207. 


Q.  3.     O=  -—  =  -—  =  0.325  ampere. 
H+r       3+3 

PAGE  209. 

Q.  i.    (7=  _JL  =  -  -15  -  =  0.048+  ampere. 
jj+r      200  +  (0.5x10) 

PAGE  210. 

E  40x1.95 


Q.  2.     C  = 


R+r      (1500 +100) +  (0.5x40) 
=  0.048+  ampere. 

Q.  3.    R=  A-  =  59. 1x^2  =  11.4+  ohms  : 
d2  165- 

C  =  -  ;  or,  0.02  = — —  ;  whence 

R  0.5  +  11.4 

E  =0.238+  volts; 
therefore  less  than  one  cell  would  be  sufficient. 


196  SOLUTIONS  TO  PEOBLEMS. 

Q.  4.     Arranged  in  multiple  arc, 


210 
arranged  in  series, 

G'  =  -  ?15  -  =  0.32+  amperes, 
(3x210)+10 

showing  that  the  latter  arrangement  is  preferable. 

10  7^ 
Q.  5.     In  this  case  the  current  C=  -  -  ;  with  one  cell 


77? 

the  current  C  = .     It  is  clear,  then,  that  if  R  is  very  smah1, 

r+R 

the  current  of  one  cell  is  about  as  strong  as  that  of  ten,  and  the 
consumption  in  the  other  nine  is  waste. 

20 
Q.  6.     C= r =  0.133+  amp&re. 

2 

Q.  7.  We  may  have  any  arrangement  in  which  the  number 
of  series  multiplied  by  the  number  of  cells  in  each  series  equals 
30 ;  e.g.,  3  rows  of  10  cells  each  ;  5  of  6  each,  etc.  Suppose, 
first,  that  the  whole  30  are  connected  in  series ;  then, 

Of) 

(a)  0  = — =  0.882+  ampere; 

(0.8x30) +10 

if  the  cells  are  joined  in  2  series  of  15  cells  each, 
15 


=  °-937+ 


if  in  3  series  of  10  cells  each, 

C  C=  =  0.789+ 


3 

It  is  easily  seen  that  with  R=  10  ohms,  the  arrangement  (b) 
is  best. 


CHAPTER    V.  —  SOUND.  197 


Let  us 
(a) 

(&) 

e») 

take  R  =  30  ohms  : 

c-        30 

=  0.555+  ampere  ; 
0.416+  ampere; 

0.306+  ampere. 

(0.8x30)  +  30 
15 

0.8x15        Q 

2 

10 

0.8X10 

3 

In  this  case  the  arrangement  (a)  gives  the  largest  value  of  C. 

In  general,  the  best  manner  of  grouping  a  given  number  of 
cells,  in  order  to  give  the  strongest  possible  current  through  a 
given  external  conductor,  is  that  by  which  the  internal  and 
external  resistances  are  as  nearly  equal  as  possible. 

Applying  this  to  tire  example  above,  we  see  that  the  internal 
resistances  (r)  in  the  three  arrangements  are  24  ohms,  6  ohms, 
and  2J  ohms ;  and  we  found  that  r  =  6  gave  the  best  result 
when  R  =  1 0 ;  and  that  r  =  24  gives  the  best  result  when 
R  ==  30,  both  of  which  agree  with  the  principle  given  above. 


CHAPTER  V. 
SOUND. 

PAGE  285.  Q.  3.  Since  the  velocity  of  sound  in  gases  is 
inversely  proportional  to  the  square  root  of '  their  densities,  the 
densities  will  be  inversely  proportional  to  the  squares  of  the 
velocities;  i.e., 

density  of  carbonic  acid :  density  of  air  :  33 12 ::  2622 ; 
or,  the  density  of  carbonic  acid  is  1.596+  times  that  of  air. 


198  SOLUTIONS   TO   PliOBLEMS. 

PAGE  293.  Q.  1.  A  fork  vibrating  256  times  per  second 
produces  wave-lengths  twice  as  long  as  those  produced  by  a 
fork  vibrating  512  times  per  second. 

Q.  2.  Wave-length  =  4  times  the  length  of  the  resonance 
tube,  or  4  X  22.26cm  =  89.04cm  =  0.8904m.  The  velocity  at  16°  C. 

is  342m  per  second;  therefore  0.8904  = — , 

number  of  vibrations 

342 
whence  the  required  number  is  =  384.09+  vibrations. 

Q.  3.     Wave-length  =  —  =  0.89m+  =  89cm. 
384 

PAGE  301.    Q.  1.     The  vibration  number  of  C"  is  528  ; 
that  of  D"  =  f     of     528  =    594 

44  44  j£"=  5.  44  44  _  QQQ 
44  44  p"  =  I  44  44  __  -Q4 
14  44  Q"  _  .1  44  44  __  yC)2 

««     "  A"=  |      "       "    =    880 

"         44     J5"=    1_5          44  44       _      99Q 

44     44  <7"=  2  times  528  =  1056 

Q.  2.  The  vibration  number  of  CLj  is  J  that  of  (7  =  £  of 
132  =  66. 


Q.  3.     Wave-length  =  -  ^  —  —  ; 

number  of  vibrations 

.-.  wave-length  of  <7  =  f||  =  1.29m-f 
»        "       «'    D'  =  ||f  =  1.15m-f 

C(  44  44  ' 


U      44      44   F' 

<t   u   u  £'  =  fff  =0.86m-f 

U  44  44  ^f__  |42_==0.77m-h 
44  '  44  4,  £'_  |||=:0.69m-f- 
44  44  44  (7"  =  |42_0>(34m_j_ 

Q.  4.  The  whole  wave-length  of  C'  we  have  found  to  be 
129cm  ;  therefore,  the  length  of  the  resonance  tube  is  £  of  129cni 
=  32.25cm. 


CHAPTER    V.  —  SOUND.  199 

PAGE  304.    Q.  3.     It  is  evident,  from  the  table  of  Fig.  21 G 
page  300,  that  the  F  string  is  f  as  long  as  the  C  string. 

PAGE  308.    Q.  1.     If  Q  and  G  are  sounded  simultaneously, 
there  will  result  for 

O,     1,  2,  3,  4,  5,  6,  7,  8,  etc.  )  ^ 

G,  |,  3,  f,  6,  9,  etc.  } times  the  number  of  vibra- 
tions made  by  the  fundamental  of  C.  From  this  arrangement, 
we  see  that  the  second  overtone  of  C  harmonizes  with  the  first 
of  G ;  the  fifth  of  C  with  the  third  of  G,  etc. 

Q.  2.     The  notes  with  their  vibration  ratios  are  as  follows  :  — 
CDEFGABQ' 

1       I       f       I       f       4      ¥      2 

Coupling  C  with  each  of  the  following,  the  ratios  of  their 
respective  vibration  numbers  are  as  follows  :  — 

8:9,  4:5,  3:4,   2:3,  3:5,  8 :  15,   1:2; 
arranging  these  on  the  required  principle,  we  have  first,  (7(1:  1) ; 
then 

C'  (1 :  2)  ;   G  (2 :  3)  ;  F  (3  :  4)  ;  A  (3  :  5)  ; 
E  (4:5);  D  (8:9);  B  (8:  15). 


CHAPTER   VI. 
LIGHT. 

PAGE  335.  Q.  1.  A  wall  of  each  of  the  rooms  would  receive 
the  same  quantity  of  light ;  viz.,  ^  of  the  total  amount. 

Q.  2.  A  wall  of  the  first  room  contains  100  sq.  ft.,  one  of 
the  third,  900  sq.  ft.  ;  since  each  wall  receives  the  same  total 
quantity  of  light,  it  is  clear  that  the  larger  one  receives  only  % 
as  much  as  the  small  one  per  square  foot. 


200  SOLUTIONS   TO   PROBLEMS. 

Q.  Sr.  We  may  look  upon  the  shadow  as  a  pyramid  of  which 
the  light  is  the  apex  and  the  boards  right  sections  ;  now,  the 
area  of  such  a  section  varies  as  the  square  of  its  distance  from 
the  apex ;  the  ratio  of  the  distances  is  1  :  3  ;  the  ratio  of  the 
areas  is,  therefore,  1:9. 

If  the  board  is  withdrawn,  the  light,  intercepted  before,  will 
illuminate  900qcm  of  the  screen. 

Q.  4.  The  reason  for  the  law  of  inverse  squares  is  involved 
in  the  answer  to  the  first  part  of  Q.  3  above. 

Q.  6.  The  ratio  of  the  distances  is  1 :  4  ;  by  the  application 
of  the  laws  of  Inverse  Squares,  the  ratio  of  the  intensities  at 
equal  distances  will  be  1  :  16,  i.e.,  the  gas  flame  may  be  said  to 
have  16  candle-power. 

PAGE  354.     Q.  2.     (a)  The  required  relative  index  equals 

absolute  index  of  diamond  _   2.5  _  .,  07, 
absolute  index  of  water         1.33 

1.000294 

(0)  The  relative  index  equals     — — — —  =  (J.7o-f-. 

l.oo 


an  opportunity  to  supplement  and  illustrate  each  other,  —  a  most 
natural  and  profitable  method  of  treatment.  He  has  actually 
demonstrated  the  practicability  of  this  plan  in  his  own  classes 
through  a  number  of  years,  and  has  moreover  proved  that  this 
study  thus  treated  begets  within  the  student  himself  a  love  for 
his  work,  which  is,  as  all  practical  educators  know,  one  of  the 
teacher's  most  potent  allies. 

In  selecting  the  material  to  be  placed  before  the  student, 
nothing  fundamentally  essential  has  been  omitted  because  of  its 
difficultness  ;  on  the  other  hand,  better  methods  of  presentation 
have  been  sought  for,  and  at  the  same  time  the  work  is  confined 
to  such  limits  that  it  may  be  accomplished  in  one  school  year. 

The  descriptive  and  qualitative  work  are  not  separated,  but 
so  intimately  blended  throughout  that  the  student  does  not 
realize  where  either  branch  begins  or  ends,  but  on  the  contrary, 
comes  to  regard  his  work  as  an  harmonious  and  logically  con- 
nected whole. 

Each  element  and  compound  is  treated  in  the  following 
natural  manner :  — 

1.  Its  occurrence,  in  which  the  student  learns  where  he  may 
find  it. 

2.  Its  preparation,  or  how  he  may  obtain  it  for  examination. 

3.  Its  properties  and  uses. 

4.  Its  tests ,  or  how  he  may  detect  its  presence  in  known  or 
unknown  substances. 

The  metals  are  classified  according  to  the  solubility  of  their 
sulphides  in  deference  to  the  analytical  features  of  the  work. 

Many  equations  are  given  to  illustrate  the  chemical  reactions 
in  the  different  operations,  and  special  directions  for  detecting 
the  acids  as  well  as  for  separating  the  metals  into  groups,  and 
isolating  the  individuals  from  each  group. 

The  work  is  to  close  with  most  full  and  explicit  directions 
for  successfully  and  economically  equipping  the  Laboratory,  and 
preparing  the  needed  re-agents  and  solutions. 

Besides  this  the  author  will  furnish  any  desired  information 
as  regards  expense,  apparatus,  chemicals,  etc.,  or  if  desired^  he 
will  supply  apparatus  and  chemicals  direct  from  the  importers, 
at  lowest  prices. 

[hi  preparation. 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
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Pamphlet 

Binder 
Gaylord  Bros.,  Inc. 

Stockton,  Calif. 
T.  M.  Reg.  U.S.  Pat. Off. 


7200 


M41814 


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